Question

determinati cel mai mic numar natural care impartit pe rand la 24, 48 si 40 da de fiecare data restul 17 si caturi nenule

Answer 1

x;24=c rest 17   ⇒   x=24c+17   ⇒ x-17=24c+17-17   ⇒x-17=24c
x:48=c rest 17   ⇒   x=48c+17   ⇒ x-17=48c+17-17   ⇒x-17=48c
x:40=c  rest 17  ⇒   x=40c+17   ⇒x-17=40c+17-17   ⇒x-17=40c

x-17=M[24,48,40]
24=2³·3
48=2⁴·3
40=2³·5
[24,40,48]=2⁴·3·5=240
M 240={240,480, 720....}
x-17=240
x=240+17
x=257
257:20=12 rest 17
257:48=5  rest 17
257:40=6 rest 17
deci cel mai mic nr.care indeplineste cond.este 257

Answer 2

n:24=a r 17 => n=27a+17 => n-17=24a => 24=2^3•3 care divide n-17/aşa faci şi cu celelalte/[24,48,40]=2^4•3•5=240/n-17=240 => n=257