Question
Let pq be a 2-digit decimal number, for example, if p=3 and q=1 then the number is 31.
Find the possible values of a, b and c, such that
ab/ba = bc/cb
and the fractions are not equal to 1.
As always, these questions are designed to be done by hand, without computational assistance. In this case, you should find some structure to the puzzle so that you can then generate many other such triangles of primes.
The first correct answer and further interesting comments will be rewarded with an upvote.
Enjoy!
- - 
- -Please Comment, Resteem and Upvote. Thanks!
@rycharde manages the AAKOM project and the MAP forum.
Also check out the new MAP Rewarder for passive income!
Thank you, @rycharde. This is interesting. I will try:
1- Based on the assumption ab = (10a+b).
Similarly bc=(10b+c), and so on.
2- Therefore (10a+b)/(10b+a)= (10b+c)/(10c+b)
=> (10a+b) * (10c+b) = (10b+a) * (10b+c)
3- Now we multiply the brackets to get:
(100 a * c ) + (10 a * b) + (10 b * c) + b^2 = 100 b^2 + (10 b * c) + (10 a * b) + (a * c)
=> 100ac + b^2 = 100b^2+ ac
=> 99 ac = 99 b^2
=> a*c = b^2
4- We know that a,b, and c are different single digit numbers. So, we can easily try what number would fit this easy formula: ac = b^2
5- Possible solutions:
Downvoting a post can decrease pending rewards and make it less visible. Common reasons:
Submit
Excellent! Upvoted.
Thanks
Downvoting a post can decrease pending rewards and make it less visible. Common reasons:
Submit
Thank you. That was really fun.
Looking forward to the next one :)
Downvoting a post can decrease pending rewards and make it less visible. Common reasons:
Submit
[Deleted]
Downvoting a post can decrease pending rewards and make it less visible. Common reasons:
Submit
That's good - gave you a small upvote :-)
but there are more solutions...
Downvoting a post can decrease pending rewards and make it less visible. Common reasons:
Submit
7.75x7.75/7.75x7.75=7.75x7.75/7.75x7.75
Downvoting a post can decrease pending rewards and make it less visible. Common reasons:
Submit
Thanks, but 7.75 is not a 2-digit number.
Downvoting a post can decrease pending rewards and make it less visible. Common reasons:
Submit
You got a 3.67% upvote from @buildawhale courtesy of @rycharde!
If you believe this post is spam or abuse, please report it to our Discord #abuse channel.
If you want to support our Curation Digest or our Spam & Abuse prevention efforts, please vote @themarkymark as witness.
Downvoting a post can decrease pending rewards and make it less visible. Common reasons:
Submit