Question

Determinați cel mai mic numar natural nenul care,impartit la 5 , 8 si,respectiv , 10, da resturile 3, 6 , respectiv 8.

Answer 1

a : 5 = x rest 3 =>a=5x+3 |+2
a : 8 = y rest 6 =>a=8y+6 |+2
a : 10 = z rest 8 =>a = 10z+8 |+2

==> a+2 = 5(x+1)
==> a+2 = 8(y+1)
==> a+2 = 10(z+1)

5 = 5
8 = 2^3
10 = 2×5
---------------
c.m.m.m.c = 2^3×5 = 40

a+2 = 40
a = 40-2
a = 38 (numarul cautat)

Verificare:
38 : 5 = 7 rest 3
38 : 8 = 4 rest 6
38 : 10 = 3 rest 8