Two numbers, x and y, are such that when divided by 6, they leave, remainders 4 and 5 respectively. Find the remainders when (x2 + y2) is divided by 6
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x = 6 * m + 4
y = 6 * n + 5
x^2 + y^2
= (36 m^2 + 16 + 48 m) + (36 n^2 + 25 + 60 n)
= 6 (6 m^2 + 6 n^2 + 8m + 10 n) + 41
so the remainder when x^2 + y^2 is divided by 6 is = 5
y = 6 * n + 5
x^2 + y^2
= (36 m^2 + 16 + 48 m) + (36 n^2 + 25 + 60 n)
= 6 (6 m^2 + 6 n^2 + 8m + 10 n) + 41
so the remainder when x^2 + y^2 is divided by 6 is = 5
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