Question

If 'n' is any natural number then find 6^n - 5^n always ends with which natural number
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Answer 1

6n−5n

For n=1

6¹−5¹=6−5=01

⇒ Unit digit is 1, i.e., ends with 1.

For n=2

6²−5² =36−25=1

⇒ Unit digit is 1, i.e., ends with 1.

For n=3

6³-5³=216−125=91

⇒ Unit digit is 1, i.e., ends with 1.

By continuity, we can say that (6n−5n) always ends with 1.

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