Question

Determinati toate numerele naturale de forma abc cu bara deasupra care impartite la ba cu bara deasupra dau catul 4 si restul bc cu bara deasupra-8

Answer 1

abc : ba =4  rest = bc-8  ba>bc-8⇒ ba+8>bc
abc=4*ba+bc-8
100*a+10*b+c=40*b+4*a+10*b+c-8
100*a+10*b+c-4*a-c=50*b-8
96*a=50*b-10*b-8
96*a =40*b-8 /:8
12*a=5*b-1

a=2⇒12*2=5*b-1⇒ 24+1=5*b⇒5b=25⇒b=25:5⇒ b=5
ba=52 , iar 52+8> 5c⇒ 60>5c⇒ c∈{0,1,2,3...,9}
nr abc sunt :250,251,252,253,254,255,256,257,258,259