© Extension of Cylclicity in GP Terms : MATHS BY AMIYA

What would be remainder if
𝑵 = 𝟐^𝟏𝟎𝟎+ 𝟐^𝟐𝟎𝟎+ 𝟐^𝟑𝟎𝟎+ 𝟐^𝟒𝟎𝟎+…+𝟐^𝟔𝟎𝟎𝟎 is divided by 7
(2 and 3 are exceptional prime)

1. What would be remainder if
𝑁 = 11^1+ 11^2+ 11^3+ 11^4+…+11^50 is divided by 13

2. What would be remainder if
𝑁 = 12^17+ 12^18+ 12^19+ 12^20+…+12^40 is divided by 5

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