Monday, 17 July 2017

Number Theory | All 4 digit palindromic numbers are divisible by 11.


Proof:
Let me suppose the number is "d1 d2 d2 d1" where d1 and d2 are digits which are used to make four digit palindrome number.

Number = 1000*d1+100*d2+10*d2+1*d1 = 1001*d1+110*d2 = 11(91*d1+10*d2).
As 11 is the factor of the number so it will be always divisible by 11.

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