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Prove that 5^6n -3^6n is divisible by 152 for n belongs to N

Prove that 5^6n -3^6n is divisible by 152 for n belongs to N

Grade:11

2 Answers

Arun
25750 Points
6 years ago
Dear Suhail
5^6n - 3^6n = (5^3n + 3^3n) (5^3n - 3^3n)
When n = 1
Then it becomes (5³ +3³) (5^3n - 3^3n) 
Hence it will be divisible by 152.
 
Regards
Arun (askIITians forum expert)
Pranav Joshi
13 Points
4 years ago
We'll go mod 152 for this.
We have [math] 5^{6n} - 3^{6n} = 15625^{n} - 729^{n}[/math]
15625 leaves a remainder 121 on being divided by 152, and so does 729. Therefore [math]15625^{n} - 729^{n} /equiv 121^{n} - 121^{n} /equiv 0 (mod 152) [/math]

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