Question

HELP ME!!! Dau coroana!!!​

Answer 1

Explicație pas cu pas:

7n+13/2n-1 €Z <=>2n-1|7n+13(divide)

2n-1|7n+13/×2=>2n-1|14n+26

2n-1|2n-1/×7=> 2n-1|14n-7

Le scadem si avem:

2n-1|14n+26-14n+7=>2n-1|33 =>

2n-1€D 33 in Z=>

2n-1€{-33,-11,-3,-1,1,3,11,33}=>

2n€{-32,-10,-2,0,2,4,12,34} =>

n€{-16,-5,-1,0,1,2,6,17}

Answer 2

7n+13/2n-1 apartine Z

Ca sa apartina lui Z trebuie ca 2n-1 sa divida pe 7n+13

2n-1 | 7n+13

2n-1 | 2n-1

inmultim mebrii de dupa | cu 2, respectiv 7

2n-1| 14n+26

2n-1| 14n-14

=> 2n-1| 14n+26-(14n-14)

2n-1|40

2n-1 apartine { -1, 1, -2, 2, -4, 4, -5, 5, -8, 8, -10, 10, -40, 40} adunam 1

2n apartine { 0, 2, -1, 3, -3, 5, -4, 6, -7, 9, -9, 11, -39, 41} impartim la 2(daca ne da fractie nu mai scriem fractia}

n apartine { 0, 1, -2, 3}

fractie apartine Z

=> n apartine {0, 1}