Question

cate nr natural de cel mult trei cifre impartite la 20 dau reestul 5.aflati suma acestora nr

Answer 1

Sunt 5 nr:
5,25,45,65,85

Answer 2

n = 20a +5 = 5(4a+1) ⇒ n = 5k  k < 200 ⇒ 4a+1 = k  4a = k-1 ⇒(k-1) divizibil cu 4 ⇒ k∈{5,9,13...197}
n ∈ {25,45,65,85.......985}.
S = 25+45+65+......+985 = 5(5+9+13+......+197)
5 = 1+4·1
9 = 1+4·2
13=1+4·3
197=1+4·49
................
S = 5(1·49 + 49·50/2 ) = 5·49(1+25) = 6370