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If r, s, t are consecutive integers, what is the greatest prime factor of 3^r +3^s + 3^t ?
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VP
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Is it 13?
Let r = k,
s = k+1
t = k +2
N = 3^k + 3^(k+1) + 3^(k+2)
= 3^k (1 + 3 + 9)
= 3^k * 13
The only prime factors of N are 3 and 13.
So 13 is the highest prime.
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VP
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giddi77 wrote: Is it 13?
Let r = k,
s = k+1
t = k +2
N = 3^k + 3^(k+1) + 3^(k+2)
= 3^k (1 + 3 + 9)
= 3^k * 13
The only prime factors of N are 3 and 13.
So 13 is the highest prime.
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Auge um Auge, Zahn um Zahn  !
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Director
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oa is 13, can you explain this part? thanks in advance.
giddi77 wrote: Is it 13?
Let r = k,
s = k+1
t = k +2
N = 3^k + 3^(k+1) + 3^(k+2)
= 3^k (1 + 3 + 9)
= 3^k * 13
The only prime factors of N are 3 and 13.
So 13 is the highest prime.
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VP
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joemama142000 wrote: oa is 13, can you explain this part? thanks in advance. giddi77 wrote: Is it 13?
Let r = k,
s = k+1
t = k +2
N = 3^k + 3^(k+1) + 3^(k+2)
= 3^k (1 + 3 + 9)
= 3^k * 13
The only prime factors of N are 3 and 13.
So 13 is the highest prime. 3^(k+1) = 3*3^k = 3*3^k
3^(k+2) = 3^2*3^k = 9*3^k
HTH
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"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."
- Bernard Edmonds
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VP
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13...as above. took the numbers as r, r+1, r+2.
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GMAT Club Legend
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If r = n, s = n+1, t = n+2
3^r +3^s + 3^t = 3^n + 3^(n+1) + 3^(n+2) = 3^n (1 + 3 + 9) = 13(3^n)
Largest prime factor = 13
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Senior Manager
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Can someone just clarify how 3^n(13) = 13 (3^n)????
My brain is hurting!
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VP
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13...
Used the same solution as above... 3^n x 13.
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CEO
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MBAlad wrote: Can someone just clarify how 3^n(13) = 13 (3^n)????
My brain is hurting!
Because r,s,t are consecutive
Let r = x
s = x+1
t = x+2
Then 3^r + 3^s + 3^t becomes
3^k + 3^(k+1) + 3^(k+2)
= 3^k + 3^k * 3^1 + 3^k * 3^2
= (3^k) * (1+3+9)
= (3^k) * (13)
Hence largest prime factor = 13
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Senior Manager
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ps_dahiya,
I just didn't understand the step "3^n(13) = 13 (3^n)" in ywilfred's post.
Does this mean a^b(c) = c(a^n)
I think I may be confusing the terms....does 3^n(13) mean 3 to the power of 13n OR 3 to the power of n, multiplied by 13?
Enlighten me!
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