Is ts solution correct, I’m not understanding the break down from the beginning. Please explain Transcribed Image Text: Inductive step: Let P (k) be true, thus 7k – 2k is divisible

Excerpt
2 (5m) = 5 [74 – 2m] Since 7k – 2m is in the set of all, we have 5 divides 7k+1 – 2k+1. Thus, P (k + 1) is true. Hence, 7″ – 2″ is divisible by 5, for each integer n > 0.

Is ts solution correct, I’m not understanding the break down from the beginning.  Please explain Transcribed Image Text: Inductive step:
Let P (k) be true, thus 7k – 2k is divisible by 8 and by the definition
of divisible, there exists an integer m such that 7k – 2k = 5m.
We need to prove that P (k + 1) is true.
7k+1 – 2k+1 = 7 · 7k – 2 · 2k

= 5- 7k + 2· 7k – 2 · 2k
%3D
= 5 – 7k + 2 [7* – 2*]
%3D
= 5- 7k + 2 (5m)
= 5 [74 – 2m]
Since 7k
– 2m is in the set of all, we have 5 divides 7k+1 – 2k+1.
Thus, P (k + 1) is true.
Hence, 7″ – 2″ is divisible by 5, for each integer n > 0.

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