Question

sa se arate ca (3n+ 5,7n +12)=1, pentru orice valoare n apartine lui N

Answer 1

3n+5,7n+12=1
 fie d un divizor comun
/ inseamna divide
d/3n+5⇒d/7*[3n+5]⇒d/21n+35
d/7n+12⇒d/3*[7n+12]⇒d/21n+36
d/21n+35, d/21n+36⇒d/21n
36-21n-35⇒d/1⇒d=1

Answer 2

d|(3n+5) |7 si d|7n+12 |3=>d|(21n+35 si d|21n+36=> d|(21 n+36-21n-35)=> d|1