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# help number theory

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Find positive integers a,b and c such that

$\dfrac38 = \frac 1{a+ \frac1{b+ \frac1c}}.$

Feb 10, 2021

#1
+31707
+3

Like so

Feb 10, 2021
#2
+112554
+1

Thanks Alan, but I have no idea what you just did.

Feb 10, 2021
#3
+31707
+3

Sorry, I shoud have provided more verbal explanation.

1st step: Invert the fraction and set 'a' to be the largest integer less than or equal to the result.

2nd step.  Subtract 'a' from the inverted fraction.  If this isn't zero

3rd step:   Repeat the first two steps with the fraction left over from step 2, to get the next constant until step 2 results in zero.

Alan  Feb 10, 2021
#4
+112554
+2

Thanks Alan,

That is super cool !

I do not ever remember seeing a problem like that one before.  I like it!

Melody  Feb 10, 2021
#5
+116125
+1

That is pretty cool   !!!!

CPhill  Feb 10, 2021