#Number or triples (a,b,c) of positive integers such that 2^a−5^b ∗7^c =1

14 messages · Page 1 of 1 (latest)

grizzled ventureBOT
hoary tendon
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Still need help with it?

gentle basin
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@hoary tendon I didn't got a clear explanation from anywhere.

hoary tendon
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Now need to do some manipulation in case one.

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I can’t solve it further rn

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After some manipulation I was able to write it as 16^a=35(k)+1 where k=5^b*7^c where a,b,c have different meaning

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And I wasn’t able to solve solutions using mod so I guess there are no solutions

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What’s the answer?

gentle basin
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no such triplet exist when 0 is not allowed. I got some seriou explanations from stackexchange which I couldn't completely understand. But this is all I understood. All the valid triplets have 0 which is not permitted

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@hoary tendon

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Tnx for your support

hoary tendon
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Can you send the link?

gentle basin
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https://artofproblemsolving.com/community/c4h2493803p21007402
https://math.stackexchange.com/questions/1181946/find-number-of-positive-integer-solution?noredirect=1
https://math.stackexchange.com/questions/3948580/if-2a-5b7c-1?noredirect=1
https://artofproblemsolving.com/community/c4h1230802p6217475
https://math.stackexchange.com/questions/1827071/number-theory-problem-finding-triplets?noredirect=1
lol many more

Mathematics Stack Exchange
Find number of Positive Integer Solution

$$2^a - 5^b7^c = 1$$
So, $a,b,c>0$.
For solving this I observed that last digit of $ 2^a$ are among any of $2, 4, 8$ and $6$ and last digit of $5^b7^c$ is always $5$ . Therefor if a is only i...

Mathematics Stack Exchange
If $ 2^a - 5^b7^c =1$ ....

Find all possible values of positive integers a, b, c such that:
$$2^a - 5^b7^c =1$$
While solving this question I surmised that a must be a multiple of 4, since $5^a7^b$ always ends with a $5$. Ad...

Mathematics Stack Exchange
number theory problem finding triplets

Find number of triplets of positive integers satisfying

$2^a-5^b\cdot 7^c=1$

Given options are $0 , 1 , 2$ or infinite.