Question
Find the remainder when 32025 is divided by
35.Solution
We can use Euler’s theorem or cyclicity. φ(35) = φ(5 × 7) = 4 × 6 = 24 So 324 ≡ 1 (mod 35), and powers repeat every 24. Compute exponent modulo 24: 2025 ÷ 24 = 84 × 24 = 2016, remainder 9 So 32025 ≡ 39 (mod 35) Now compute 39 mod 35: 3¹ = 3 3² = 9 3³ = 27 3⁴ = 81 ≡ 81 − 70 = 11 3⁵ = 11×3 = 33 3⁶ = 33×3 = 99 ≡ 99 − 70 = 29 3⁷ = 29×3 = 87 ≡ 87 − 70 = 17 3⁸ = 17×3 = 51 ≡ 51 − 35 = 16 3⁹ = 16×3 = 48 ≡ 48 − 35 = 13 Remainder = 13.
The essential amino acid in short supply in cereals is:
Aroma in scented rice is due to the presence of
PM Modi’s Tricolour Revolution are associated with…………………………..
National Institute of Biotic Stress Management was established at which place and in which year?
The element used in the manufacture of safety matches is —
What are the basic steps involved in information management?
Which among the following is monophagous insect pest?
Which one of the following CANNOT be called a Non-Communicable Disease?
Which Fish has the highest protein content?
The yellow vein mosaic of okra is majorly transmitted by ____
Relevant for Exams:
