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Saltyone
a fost răspuns

Scrieti numarul 41 la puterea 2009 ca suma de doua patrate perfecte diferite. Va rog!

Răspuns :

41^2009=41×41^2008
=(16+25)×41^2008
=16×41^2008+25×41^2008
=4^2×41^2008+5^2×41^2008
=(4×41^1004)^2 +(5×41^1004)^2
Albatran
41^2009=41*41^2008=(25+16)*(41^1004)²=(5²+4²)*(41^1004)²=
=5²*(41^1004)²+4² *(41^1004)²=
(5**41^1004)²+(4*41^1004)²=a²+b² suma de 2 patrate perfecte


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