Find the remainder when 935¹²³ divided by 39

Question

Question

This question was previously asked in

UP Police SI (दरोगा) Official PYP (Held On: 16 Nov 2021 Shift 3)

Answer 1

Given:

Find the remainder when 935¹²³ is divided by 39

Formula used:

Using modular arithmetic:

Where, can be simplified using properties of modular arithmetic.

Calculations:

Simplify 935 mod 39

⇒ 935 ÷ 39 = 23 remainder 38

⇒ 935 mod 39 = 38

Use modular arithmetic to calculate 38¹²³ mod 39

Note: 38 ≡ -1 (mod 39)

⇒ 38¹²³ mod 39 ≡ (-1)¹²³ mod 39

⇒ (-1)¹²³ = -1

⇒ -1 mod 39 = 38

∴ The correct answer is option (2).

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