Question

Sa se determine numerele naturale mai mici sau egale cu 500 care impartite pe rand la 8,15,24 dau caturi nenule si resturile 5,4 respectiv 13.

Answer 1

n=8xc1+5=15xc2+4=24xc3+13
n+11=8xc1+16=15xc2+15=24xc3+24
n+11=8(c1+2)=15(c2+1)=24(c3+1)
n+11=M [8,15,24]=M 120
n+11={120,240,360,480}
n={109,229,349,469}

Answer 2

x:8=ar 5
x:15=br4
x:13=cr13
conf Thomas împărțirii cu rest
x=8a+5
x=15b+4
x=24c+13
x=8a+16-11
x=15b+15-11
x=24c+24-11
x+11=8(a+2)
x+11=15(b+1)
x+11=24(c+1)
cmmmc [8,15,24]=2^3×4×5=120
M120={120,240,360,480,600,720,.....}
luam valorile<500
x+11=120
x=120-11
x=109
x+11=240
x=229
x+11=360
x=349
x+11=480
x=469