Consider the set $A$ = {${-6, -5 -4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,11,12}$}
Write down the numbers in $A$ congruent to $1$ modulo $4$.
Can someone explain why the answer is not $-4,-1,-4,8,12$ but instead $−3, 1, 5, 9$.
2026-03-26 06:25:47.1774506347
Explanation of congruence and modulo
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You just need to verify the definition : $$a \equiv b \pmod n \iff n | (a-b)$$
$$a \equiv 1 \pmod 4 \iff 4 | (a-1)$$
What numbers in the given list are divisible by $4$ after subtracting $1$ ?