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Find the prime number $p$, for which the sum of the digits of the number $f(p^2+

Source: Moldova TST 2022

April 1, 2022
number theory

Problem Statement

Let f:N→N,f:\mathbb{N} \rightarrow \mathbb{N}, f(n)=n2−69n+2250f(n)=n^2-69n+2250 be a function. Find the prime number pp, for which the sum of the digits of the number f(p2+32)f(p^2+32) is as small as possible.
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