real numbers

[sharu]

HCF of (65,117) is 13 then express it in the form 65m+117n where m and n are integers?

[kiran_ghosh]

the answer is m=2 and n=-1
this came in the int maths olympiad

[karansharma]

the best thing u can do is ask ur teacher.

[sharunn]

117=65 * 1 + 52 --------(1)
65=52 * 1 + 13 -----(2)
52=13 * 4 + 0 -----(3 )
So HCF=13
now,

13= 65 - ( 52 * 1) {from (2)}

but 52= 117 - (65 * 1) {from(1)}


so
13 = 65 - { 117 - (65*1)}
13= 65 -117 + 65
13 = {65 * 2} + {117 * (-1)}
where m=2 and n= -1


SO in which school do u study