A number theory problem by Adrian Gonzalez
Let a , b and c positive integers such that a and b are odd. What is the residue of divided by 4?
The answer is 3.
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1 solution
For b-1^{2}, b is odd so the square of any even number will be divisible by 4. Then use binomial expansion by writing 3 as 4-1. So we get remainder as -1. Since remainders are positive, it will be 3.