Question

What is the remainder when 19 95 is divided by 362 ?

Answer 1

• When 19⁹⁵ is divided by 362, remainder is equal to 343 .

To Find :- The remainder when 19⁹⁵ is divided by 362 ?

Solution :-

→ 19⁹⁵ ÷ 362

→ 19^(92 + 3) ÷ 362

using a^(m + n) = a^m × a^n,

→ (19⁹² × 19³) ÷ 362 ------ Equation (1)

now,

→ (19²) = 361

So,

→ (19²) ÷ 362

→ 361 ÷ 362 = (-1) remainder

then,

→ (19²)² ÷ 362 = (-1)² = 1 remainder

therefore,

→ 19⁹² ÷ 362 = (19²)⁴⁶ ÷ 362 = (-1)⁴⁶ = 1 remainder ------ Equation (2)

putting Equation (2) in Equation (1) we get,

→ (1 × 19³) ÷ 362

→ (19² × 19) ÷ 362

→ (361 × 19) ÷ 362

→ (-1 × 19) ÷ 362

→ (-19) ÷ 362

hence,

→ Required remainder = 362 - 19 = 343 (Ans.)

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