Would LWE problem be still secure if error were like this $e=2e_1$? In the Learning with error problem, if the error term $e$ from equation $b=&lt;a,s&gt;/q+e$ were of this kind $e=2e_1$, where $e_1$ is chosen according to the probability distribution for the LWE problem, it would weaken the problem significantly or the security insured would remain the same ?
It will remain same. Here it will not effect the security because 2 is invertible in the prime q field. In case q is not prime then security will be compromised.