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Use the Principle of Mathematical Induction (PMI) to prove that the following statement is true for all natural numbers n: 7 divides 15^n + 6

Use the Principle of Mathematical Induction (PMI) to prove that the following statement is true for all natural numbers n: 7 divides 15^n + 6

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Use the Principle of Mathematical Induction (PMI) to prove that the following
statement is true for all natural numbers n:
7 divides 15^n + 6

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The expression "7 divides \(15^n + 6\)" indicates a mathematical statement where 7 is a divisor of the expression \(15^n + 6\). This means that when \(15^n + 6\) is divided by 7, the remainder is 0. Here, \(n\) is typically considered as a non-negative integer, serving as the exponent of 15. This problem involves number theory concepts related to divisibility and modular arithmetic.
Transcribed Image Text:The expression "7 divides \(15^n + 6\)" indicates a mathematical statement where 7 is a divisor of the expression \(15^n + 6\). This means that when \(15^n + 6\) is divided by 7, the remainder is 0. Here, \(n\) is typically considered as a non-negative integer, serving as the exponent of 15. This problem involves number theory concepts related to divisibility and modular arithmetic.
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