Olympiad Maths Prep

Track / Stage 4 / 234 of 340 #494 of 2000

Problem 494

AMC 12 late, AIME early
Number theory Difficulty 4.9 Find the answer

Let's determine all natural numbers x x for which

p(x)=x2−10x−22, p(x) = x^2 - 10x - 22,

where p(x) p(x) represents the product of the digits of the number x x written in the decimal system.

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

Official solution

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