Question

Sa se arate ca daca a | a*b+c si a | a*c+b, atunci a | $\frac{}{bc}$ + $\frac{}{cb}$

Answer 1

a  divide( ab +c )⇒ a divide (abc +c²)

a divide( ac+b)⇒a divide (abc+ b²) ⇒⇒ a divide (abc+ b²)-(abc +c²)= b²-c²=(b+c)(b-c)

bc+cb=10b+c +10c +b=11b +11c=11(b+c) ; a divide (b+c) ⇒⇒a divide bc+cb