Question

Determinati toate numerele naturale mai mari decat 500 care impartite la 25 au restul si catul egale intre ele.

Answer 1

d:i=c si r  si r<i si r=c
d:25=c conform teoremei impartirii cu rest⇒d=25·r+r⇒d=26·r dar r<25

luam cazurile
r=0⇒d=0 caz imposibil
r=1⇒d=26·1=26 nu merge <500
r=2⇒d=26·2=52 nu merge <500
......................
r=19⇒d=26·19=494 nu merge <500
r=20⇒d=26·20=520
r=21⇒d=26·21=546
r=22⇒d=26·22=572
r=23⇒d=26·23=598
r=24⇒d=26·24=624

Answer 2

n = 25c +r      r=c      r < 25    n = 25r + r = 26r  26r > 500 ⇒r≥20 ⇒ r∈{20,21,22,23,24} ⇒n∈{520,546,572,598,624}