Question

aflati abc stiind ca impartit pe rand la 15, 12 si 80 da restul 10 ,7 respectiv 75

Answer 1

n=abc
n:15=c1 r 10, n=15c1+10=15c1+15-5=15(c1+1)-5
n:12=c2r 7, n=12c2+7=12c2+12-5=12(c2+1)-5
n:80=c3 r 75, n=80c3+75=80c3+80-5=80(c3+1)-5
rezulta ca n+5=M15=M12=M80
calculez [15,12,80]
15=3*5
12=2^2*3
80=2^4*5
[15,12,80]=2^4*3*5=240
rezulta ca n+5 e multiplu de 240
n+5∈{240,480,720,960}
n∈{235,475,715,955}