Question

Find the smallest prime number dividing the sum 3¹¹+5¹¹

Answer 1

Question

Find the smallest prime number dividing the sum 3¹¹+5¹¹

ANSWER

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The Last Digit of 3¹¹ = 7 ( Since Last digit of power of 3 repeats a cycle of 3,9,7,1 )

The Last Digit of 5¹¹ = 5 ( Since Last digit of power of 5 is always 5)

Last Digit of 3¹¹ + 5¹¹ is (7+5)

Last Digit of 3¹¹ + 5¹¹ is (last digit of 12)

Last Digit of 3¹¹ + 5¹¹ is 2

Hence their sum is even

Therefore smallest Prime Number dividing their Sum is 2.

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