This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 2

1973 All Soviet Union Mathematical Olympiad, 175
Tags: perfect square , 9-digit , number theory
Prove that $9$-digit number, that contains all the decimal digits except zero and does not ends with $5$ can not be exact square.

1983 Tournament Of Towns, (050) 2
Tags: number theory , 9-digit , sum
Consider all nine-digit numbers, consisting of non-repeating digits from $1$ to $9$ in an arbitrary order. A pair of such numbers is called “conditional” if their sum is equal to $987654321$. (a) Prove that there exist at least two conditional pairs (noting that ($a,b$) and ($b,a$) is considered to be one pair). (b) Prove that the number of conditional pairs is odd. (G Galperin, Moscow)