$$
This implies
$$
y = \pm \bigg({1 \over 3} \sqrt{2^{n + 3} 5^{n} - 71}\bigg)
$$
The term under the radical needs to be a perfect square for $y$ to be an integer and also a multiple of $9$. $\text{i.e.,} \exists x \in \mathbb{Z}$ such that,
$$
2^{n + 3} 5^{n} - 71 = (3x)^2
$$
Case 1 ($n$ is even):
Since $n$ is even, we may take $n = 2m$ and rewrite the equation as
$$
2^3(10)^{n} - 71 = (3x)^2 \\
\implies 2^3(10)^{2m} - 71 = (3x)^2 \\
\implies 8(10^m)^{2} - 71 = (3x)^2
$$
Taking $10^m = Y, 3x = X$,
$$
8Y^{2} - X^2 = 71
$$
This is a Pell equation.
Case 2 ($n$ is odd):
Since $n$ is odd, we may take $n = 2m+1$ and rewrite the equation as
$$
2^3(10)^{n} - 71 = (3x)^2 \\
\implies 2^3(10)^{2m+1} - 71 = (3x)^2 \\
\implies 80(10)^{2m} - 71 = (3x)^2 \\
\implies 80(10^m)^{2} - 71 = (3x)^2
$$
Taking $10^m = Y, 3x = X$,
$$
80Y^{2} - X^2 = 71
$$
This is also a Pell equation.
We may solve those Pell equations to find solutions for $n$.
The Nature Play Family Geo­Challenge is an exciting family weekend event full of outdoor activities for all ages. We’ve hidden loads of geocache canisters around the National Park and we will provide your family with the event link for your smartphone, clues and instructions to find them. This self­-guided geocaching experience is a great chance for your family to share an outdoor adventure at your own pace in WA’s majestic Margaret River region. It’s not a race, but you can win prizes just for participating!
Where: Wharncliffe Mill Bush Retreat, Margaret River.
This text leads us on a journey through five revolutions in geometry, via biographical stories, from the Greek concept of parallel lines to contemporary notions of hyperspace. It reveals simple questions that have been the hidden engines of major achievements in science and technology.
Leonard Mlodinow, PhD, was a member of the faculty of the Californian Institute of Technology before moving to Hollywoos to become a writer for televsion. He has developed many best seliing and award-winning CD-ROMs and is currently VIce President,Emerging Technologies and R&D at Scolastic Inc. He lives in New York City.

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If you need a product to make an impact a full colour picture mug is the perfect solution. Using dye sublimation printing, which is a combination of the intense heat and pressure allowing the ink to vaporise and permanently colour the mug, with your promotional logo. The cups are available in a number of styles including latte and heat sensitive and the photo can cover almost all of the mugs surface area. Every photo mug is both dishwasher and microwave safe and if you want to make a lasting impression, then we recommend you choose these stylish mugs.Have You Considered A Plasma TV?
Plasma TVs have hit an all time high and are more popular now than ever.
Stores are changing up their stock to accommodate plasmas, leaving consumers in a fury to decide which television to purchase in which size and style.
Before purchasing anything of this size it is highly advisable to learn as much as you can about it so you know what you're getting into, especially since it will be a costly investment.
Before buying that new plasma television, or if you just want to brush up on some new technology, you'll need to be introduced to the basics and some special quirks of the new rage known as plasma TVs.
First you should learn some information about the workings and what makes the plasma television tick.
All plasmas are flat display panels.
They've gotten the name plasma because the pixels are generated by plasma cells, also known to be in fluorescent lamps.
Between the glass panels of each plasma TV there are millions of these little cells mixed up with noble gases and very small amount of mercury in compartmentalized spaces.
This strange mixture creates a reaction when given power, which makes it form into a plasma.
An interesting fact to remember is that every pixel in a plasma display panel is made of a total of three cells compromising the colours of light.
With all of the reactions going on inside, the plasma TV becomes one of the best televisions on the market right now.
The display on a plasma is very bright and has a wide colour gamut, but the best part is that it can be produced in very large sizes.
It can be bought in sizes up to 150 inches from side to side, but average sizes range from 32 inches to 63 inches.
Generally the thickness of one of these is about 2.
5 inches thick, or less than four inches.
It doesn't use very much power either, but power usage strongly depends on how bright the scenes displayed are.
Typically brighter scenes will use more power than darker ones.
The darker scenes are thought to be very superb, because it produces very deep blacks.
The screen is made of glass, which is more reflective unless technology such as anti-glare filter material is used.
Currently in the market, the plasma TV has the best viewing angles which produce the greatest brightness and contrast in a variety of angles.
They're recommended a lot more for gamers, because it's able to refresh and handle rapidly moving images fast.
There is no motion blur unlike some of the other leading TV types on the market right now.
These televisions have a life span between 30,000 hours to 60,000 hours.
One of the good points of it is that it can be wall mounted.
Make sure you're careful when installing them on a wall, because plasmas are very fragile and can break easily.
When buying a new plasma keep in mind that they do not normally come in sizes smaller than 37 inches, and they are very susceptible to screen burn-in.
Other than that, it can be said that the plasma TV is one of the best televisions on the market right now.Creating randomized prophecies/fortunes for my players?

I'm in the writing process for a campaign I'm starting up in a couple months. I have the basics of the first mini-arc planned, but I've had an idea rattling around in my brain. I'd like to introduce the PC's to some kind of seer or fortune telling NPC who I would use to plant seeds for future plot hooks or give them some insight into the possible outcomes of their actions.

The way I had planned for this NPC to work is that she (Really me as the GM) would roll a set of dice ('Casting the bones' as the in-game term.) ranging from d4 to possibly d8, with the number and type of dice indicating the length and possibilities of the prophecies. Each die would be assigned to a part of a prophecy, allowing for me to randomize the outcomes and keep things vague enough to interpret multiple ways, if I play it right.

My problem is this: Though I have an idea on the mechanics of how this would work, I can't seem to work out A) The different sections/types of prophecies, and B) Ideas for specifics on the prophetic elements. Feedback of any kind is appreciated on this, including if you think this is just a bad idea and I should give it up!Radiology Assistants/Radiology Receptionists perform all front office functions which include answering the phones and directing customers correctly and effectively. Process all paperwork, i.e. prescriptions/requisitions, and procedure orders. Schedule all patient examinations. Radiology Assistants/Radiology Receptionists process exam reports and act as the liaisons with the hospital staff and the Imaging Staff where ever needed, as appropriate to the task.
• Interacts and registers all out-patients.
• Schedules Examinations as needed.
• Properly educate patients and families to radiologic procedures and preparations to examinations.
• Accurately sorts, distributes and mail copies of all imaging reports. Collects, generates, analyzes, and distributes statistical date as required.
• Provides Patients, families and physicians with information as needed.
• Manages the Subpoena file as appropriate, logging requisitions, retrieving images, creating CDs, etc.
• May be asked to transport patients.
• Performs any other duties or responsibilities as assigned.
October, means fall weather has officially arrived in Austin, Texas. The days begins to chill down, and our lows scratch the surface of 60s during the nights and mornings, and highs of 80s and 70s when it’s bright and sunny. For this entry I observed an extension of Walnut Creek which leads through the backyards of many people in my neighborhood. I wanted to compare general differences in wildlife when nature is closer to human development which potentially, could have greater