Third Problem, Danube Mathematical Competition 2012
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Laurențiu Ploscaru
- Mesaje: 1237
- Membru din: Mie Mai 04, 2011 5:42 pm
- Localitate: Călimănești
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Third Problem, Danube Mathematical Competition 2012
Let $p$ and $q,\ p<q$, be two primes such that $1+p+p^2+...+p^m$ is a power of $q$ and $1+q+q^2+...+q^n$ is a power of $p$, for some positive integers $m$ and $m$. Prove that $p=2$ and $q=2^t-1$ where $t$ is a prime number.
People are strange when you're a stranger,
Faces look ugly when you're alone.
Women seem wicked when you're unwanted,
Streets are uneven when you're down.
Faces look ugly when you're alone.
Women seem wicked when you're unwanted,
Streets are uneven when you're down.