3^{90} + 5^{90} can be written as (3^{2})^{45} + (5^{2})^{45}
= (9)^{45} + (25)^{45}
Any number of the form a^{n} + b^{n} is a multiple of (a + b) whenever n is odd.
So (9)^{45} + (25)^{45} is a multiple of 9 + 25 = 34
So, the remainder when we divide (3^{2})^{45} + (5^{2})^{45} by 34 is equal to 0.
Correct Answer: 0