Question

a positive integer m divides 748x+714y for all values of x and y .how many values of m can we have ?

Answer 1

linear combination of 748 and 714

Answer 2

:O , i didnt understand

Answer 3

4 values of m

Answer 4

can u explain how you got this?

Answer 5

what is the answer?

Answer 6

i dont know but the options are :-

1)2
2)3
3)4
4) infinitely many

Answer 7

748x+714y=748(1)+(-1)714

Answer 8

m can be 1,2,17,34

Answer 9

firstly note that the greatest common divisor of 748 and 714 is 34 because:
\[748=2^2*11*17\]\[714=2*3*7*17\]now we know that m divides\[34(22x+21y)\]for all values of x and y specially for x=1 and y=-1 which will gives the number as\[34(22-21)=34\]so m must be a divisor of 34 and since we know 34=2*17 so\[m=1,2,17,34\]

Answer 10

we let x=1 and y=-1 because we want to make the 22x+21y equal to 1

Answer 11

thanks ! it really helps :)

Answer 12

yw :)