when 6^83+8^83 is divided by 49 , tell the remainder left where ^ denotes raised to?

Express this equation as

(7-1)⁸⁹ + (7+1)⁸⁹.

This will give 

= (⁸⁹C₀7⁸⁹-⁸⁹C₁7⁸⁸+⁸⁹C₂7⁸⁷+...-⁸⁹C₈₇7²+⁸⁹C₈₈7¹-⁸⁹C₈₉7⁰)+(⁸⁹C₀7⁸⁹+⁸⁹C₁7⁸⁸+⁸⁹C₂7⁸⁷+...-⁸⁹C₈₇7²+⁸⁹C₈₈7¹-⁸⁹C₈₉7⁰)

=2*(⁸⁹C₀7⁸⁹+⁸⁹C₂7⁸⁷+⁸⁹C₄7⁸⁵+...+⁸⁹C₈₆7³+⁸⁹C₈₈7¹)

⁸⁹C₀7⁸⁹+⁸⁹C₂7⁸⁷+⁸⁹C₄7⁸⁵+...+⁸⁹C₈₆7³ will all be divisible by 49 because they consist of 7² as one of their factor but not 2(⁸⁹C₈₈7¹)

Then 2(⁸⁹C₈₈7¹)%49 = 21 ---Remainder

sorry for my mistake, its (7-1)⁸³ + (7+1)⁸³ not (7-1)⁸⁹ + (7+1)⁸⁹.

In similar ways of my prev reply  the remainder will be  2(⁸³C₈₂7¹)%49 =35