Number and Algebra
Functions
Geometry & Trigonometry
Statistics & Probability
Calculus
Prove by induction that 3 divides 4n−14^n - 14n−1 for all integers n≥1n\ge1n≥1.
Prove by induction that n3−nn^3 - nn3−n is divisible by 666 for all integers n≥1n\ge1n≥1.
Prove by induction that 7 divides 8n−18^n - 18n−1 for all integers n≥1n\ge1n≥1.
Prove by induction that 9 divides 10n−110^n - 110n−1 for all integers n≥1n\ge1n≥1.
Prove by induction that 6 divides 7n−17^n - 17n−1 for all integers n≥1n\ge1n≥1.
Prove by induction that 13 divides 14n−114^n - 114n−1 for all integers n≥1n\ge1n≥1.
Prove by induction that 31 divides 25n−12^{5n} - 125n−1 for all integers n≥1n\ge1n≥1.
Prove by induction that 7 divides 62n−16^{2n} - 162n−1 for all integers n≥1n\ge1n≥1.
Prove by induction that 15 divides 24n−12^{4n} - 124n−1 for all integers n≥1n\ge1n≥1.
Prove by induction that 5 divides 32n+1+2n+23^{2n+1} + 2^{n+2}32n+1+2n+2 for all integers n≥1n\ge1n≥1.
Prove by induction that 13 divides 312n−13^{12n} - 1312n−1 for all integers n≥1n\ge1n≥1.
Prove by induction that 17 divides 28n−12^{8n} - 128n−1 for all integers n≥1n\ge1n≥1.
Prove by induction that 11 divides 52n+22n+15^{2n} + 2^{2n+1}52n+22n+1 for all integers n≥1n\ge1n≥1.
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Question Type 4: Using induction for proving equalities
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