Question

aflati doua numere naturale a si b daca a +b= 40 si (a;b) =5​

Answer 1

a + b = 40

( a, b ) = 5 => a = 5x, b = 5y cu condiția ca ( x, y ) = 1

5x + 5y = 40

5 × ( x + y ) = 40 | : 5

x + y = 8

=> ( x, y ) = { ( 1, 7 ), ( 3, 5 ), ( 5, 3 ), ( 7, 1 ) }

=> ( a, b ) = { ( 5, 35 ), ( 15, 25 ), ( 25, 15 ), ( 35, 5 ) }