Q) Find the remainder obtained when 43^101 + 23^101 is divided by 66?
Altought we can use the relation
Bs is the s-th Bernoulli Number
(100-th Bernoulli Denominator is )
(Look Bernoulli Numbers Fundamental Theorem of Arithmetic (in google) for details),
A simpler approach is:
Look here for this factorization
The last expression obviously is divisible by 66, so: