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  4. If R is remainder when 683+883 is divided by 49 then R / 5=

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Q. If $R$ is remainder when $6^{83}+8^{83}$ is divided by 49 then $R / 5=$

Binomial Theorem

Solution:

Given $=(7-1)^{83}+(7+1)^{83}=(7+1)^{83}-(1-7)^{83}$ $=2.7 .83+49 I , I$ is integer
$=49 I +23 \times 49+35 \therefore R =35$
$\therefore R / 5=7$