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Q77·CSAT · Prelims 2025

Remainder of 9^3+9^4+...+9^100 mod 6

NumericalRemainders & CyclicityNumber theoryHard

Question

What is the remainder when 2^1 9^3 + 9^4 + 9^5 + 9^6 + ... + 9^{100} is divided by 6?

Options

a

0

Answer
b

1

c

2

d

3

Explanation

Every 9^k mod 6 = 3, there are 98 terms, 98 × 3 = 294, 294 mod 6 = 0 Answer: (a).

Question details

Year

2025

Paper

CSAT

Question

Q77

Section

Numerical Ability

Sub-topic

Remainders & Cyclicity

Type

Number theory

Difficulty

Hard

Source hint

Number theory

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