Put a=11¹³. Modulo a+1, a≡−1, so $a^4-1\equiv1-1=0$. Therefore $11^{52}-1$ is divisible, giving **D**. A gives remainder2 and C gives−2;33 is not an odd multiple of 13, so the usual odd-power factorization does not apply to B.
More Quantitative Aptitude: Algebra, Geometry and Mensuration questions
GATE 2026 ES Q10– Three externally tangent circles C 1,C 2,C 3 have centers O 1,O 2,O 3 and radii r 1=2 cm,r…
GATE 2025 ES Q5– A rectangle has a length L and a width W, where L > W. If the width, W, is increased by…
GATE 2025 ES Q8– A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius r cm as…
GATE 2025 ES Q9– If a real variable x satisfies 3x2 = 27 9x, then the value of 2x2(2x)2 is:
GATE 2024 ES Q4– The sum of the following infinite series is 2 + 12 + 13 + 14 + 18 + 19 + 116 + 127 +
GATE 2023 ES Q3– Given a fair six-faced dice where the faces are labelled ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, and ‘6’,…