Parity of Nth Term in Fibonacci Integer Sequences
Python, 29 bytes

lambda a,b,n:[a,b,a+b][n%3]%2

The generalized Fibonacci sequence modulo 2 has cycle length of 3. So, we reduce n mod 3 and take that element of the first three.

31 bytes:
lambda a,b,n:0&lt;a%2*2+b%2!=n%3+1

True for odd, False for even