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Use mathematical induction to show that 4^n ≡ 3n+1 (mod 9) for all n equal to or greater than 0
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Use mathematical induction to show that 4^n ≡ 3n+1 (mod 9) for all n equal to or greater than 0
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Jan 26, 2018
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Use mathematical induction to show that 4^n ≡ 3n+1 (mod 9) for all n equal to or greater than 0
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When
, you have
Now assume this is true for
, i.e.
and under this hypothesis show that it's also true for
. You have
In other words, there exists
such that
Rewriting, you have
and this is equivalent to
modulo 9, as desired.
Shonali
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Jan 31, 2018
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Shonali
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