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Arata ca 1+5+5 la puterea 2+....+5 la puterea 101 se divide cu 31

Răspuns :

nr.de termeni (104-0)+1=105 termeni care se pot grupa cate 3⇒35 de grupe
5⁰+5¹+5²+5³+..............+5¹⁰⁴| 31
(1+5+5²)+5³(1+5+5²)+.........+5¹⁰²(1+5+5²)
(1+5+5²)(1+5³+5⁶+..............+5¹⁰²)
1+5+25=31
31(1+5³+5⁶+.......+5¹⁰²)|31