The number of ordered pairs (m,n) m,n€{1,2,3,...,100} such that 7 m +7 n is divisible by 5 is ___

Question

Deepak Kumar Shringi · Answer

to divisible by 5 unit digit must be either zero or 5 here exponent of 7 can be
(7,9,3,1) at unit digit and to make sum 0 or 5 it should be
(7+3) or (9+1)
to take 7+3
(7¹+7³) and (7⁵+7³)...................................(7⁹⁹+7³)

(7¹+7⁷)...........................................................(7⁹⁹+7⁷)
in this way you can apporach it

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The number of ordered pairs (m,n) m,n€{1,2,3,...,100} such that 7 m +7 n is divisible by 5 is ___

The number of ordered pairs (m,n) m,n€{1,2,3,...,100} such that 7^m+7ⁿ is divisible by 5 is ___

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The number of ordered pairs (m,n) m,n€{1,2,3,...,100} such that 7 m +7 n is divisible by 5 is ___

The number of ordered pairs (m,n) m,n€{1,2,3,...,100} such that 7m +7n is divisible by 5 is ___

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The number of ordered pairs (m,n) m,n€{1,2,3,...,100} such that 7^m+7ⁿ is divisible by 5 is ___