Discussion on International Mathematical Olympiad (IMO)
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if $a,b,c,d$ are natural numbers and $ab=cd$,then,prove that,$a+b+c+d$ cannot be a prime.
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Try to prove the general one.
If $ab=cd$, prove that $a^n+b^n+c^n+d^n$ is not prime.
One one thing is neutral in the universe, that is $0$.
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The following method works for many problems of similar sort.
"Everything should be made as simple as possible, but not simpler." - Albert Einstein