Question

1^13+2^13+3^13....60^13 is divisible by?

Answer 1

Heya User,

--> We know that --> a + b | aⁿ + bⁿ ∀ n ∈ odd natural no.s

--> Hence,
          1¹³ + 2¹³ + 3¹³ + 4¹³ + ... + 60¹³
------> ( 1¹³ + 60¹³ ) + ( 2¹³ + 59¹³ ) + ... + ( 30¹³ + 31¹³ )

However, 13 is odd, and :-> 
--> ( 60 + 1 ) divides ( 60¹³ + 1¹³ ) ...
--> ( 59 + 2 ) divides ( 59¹³ + 2¹³ ) and so on..

Hence, 61 divides the sum ... 

Answer 2

Answer:

one of the correct answer is 61