Find that minimum value of x

Number Theory Level 3

Positive integer $x$ is such that the remainder of $x^{2}$ when divided by 9 is 7. If $x>23$ , what is the minimal value of $x$ ?

The answer is 31.

1 solution

Jared Low
Nov 15, 2018

For positive integers $x$ , $x^2$ leaves a remainder of 7 when divided by 9 if and only if $x \equiv 4, 5 \pmod{9}$ . The sequence of such numbers is $4,5,22,23,31,32, \ldots$ , the minimal value of which that exceeds 23 being $\boxed{31}$

Find that minimum value of x

The answer is 31.

1 solution

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