Question

Aflatii cel mai mic nr natural de 3 cifre care impartit la 3, 4, 5 da restul 2,3,4 ?

Answer 1

n =nr

n:3 r2 rez n=3*a+2=3*a+3-1=3*(a+1)-1 deci n+1=3*(a+1)

n:4 r3 rez n=4*b+3=4*b+4-1=4*(b+1)-1 deci n+1=4*(b+1)

n:5 r4 rez n=5*c+4=5*c+5-1=5*(c+1)-1 deci n+1=5*(c+1)

n+1 se divide cu 3.4.5 deci si cu cmmmc adica 60
n+1 apartine multiplilorlui 60 adica 0.60.120,........
n apartine 59,119.......
deci n=59