# Eikonal Blog

## 2010.01.05

### Number theory finite concidental sums

Filed under: mathematics, number theory — Tags: — sandokan65 @ 15:43

$1+3+3^n+3^{n+1}+3^{2n} = (2+3^n)^2$

$1+3^n+3^{n+1}+3^{2n} +3^{2n+1}= (1+2 \cdot 3^n)^2$

$1+7+7^2+7^3=20^2$

$1+12^2+12^3+12^4+12^5=521^2$

Reference: T1277

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