Arberi1 22.04.2012 23:41 Find all three digit numbers, for which the sum of squares of each digit is $90$ .
VIPMaster 23.04.2012 00:10 Hint Note that at least one of the digits must be greater than $5$. Simple casework (which I don't want to bother with right now) finishes the problem.
BISHAL_DEB 23.04.2012 14:32 Another way: Notice by going mod $4$ that two are odd and one is even. WLOG assume that $c$ is even and can hold values of $0,2,4,6,8$. Analyse each case. Answer: $16$
SCP 30.04.2012 20:35 $90=9^2+3^2+0^2$ $=7^2+4^2+5^2$ $=8^2+5^2+1^2$ Permutation of the numbers give the $16$ values.