Question
What is the remainder when 32025 is divided
by 7?Solution
ATQ, Powers of 3 modulo 7: 3¹ ≡ 3 3² ≡ 9 ≡ 2 3³ ≡ 3·2 = 6 3⁴ ≡ 3·6 = 18 ≡ 4 3⁵ ≡ 3·4 = 12 ≡ 5 3⁶ ≡ 3·5 = 15 ≡ 1 (mod 7) So, 3⁶ ≡ 1 (mod 7), cycle length 6. 2025 ÷ 6 = 337 remainder 3. So 3^2025 ≡ 3³ (mod 7) ≡ 27 ≡ 6 (mod 7).
More No. System Questions
If x - 1/x = 9, then the value of x² + 1/ x² is:
- Simplify the following expression:
16 + [17 - (8 + 11) + 6 - 3] ÷ 0.2 ((1024)n/5 × (42n+1 ))/(16n × 4n-1 ) = ?
420 ÷ 7 + 140 % of 20 + ? × 13 = 18 × 15
What will come in place of the question mark (?) in the following expression?
(320 ÷ 8 + 22) × 4 = 60 + 40% of ?
2/5 of 3/4 of 7/9 of 14400 = ?
Simplify the given expression:-
46% of 13/92 × 24/91 × 3500 =?
