Question

If `R` is remainder when `6^(83)+8^(83)` is divided by 49, then the value of `R//5` is.

Answer 1

Correct Answer - 35
`(1+7)^(85) + (7-1)^(83) = (1+7)^(83) - (1-7)^(83)`
`= 2[.^(83)C_(1).7+.^(83)C_(3).7^(3)+"….."+.^(83)C_(83).7^(83)]`
`= (2.7.83) + 49I` where I is an integer
Now `14 xx 83 = 1162`
`:. 1162/49 = 23(35)/(49)`
`:.` Remainder is `35`