Find-all-integer-solutions-of-3-m-2n-2-1-I-only-found-m-1-2-5-by-computer-from-m-1-to-m-30000-Is-there-any-greater-solutions-

Question Number 216538 by CrispyXYZ last updated on 10/Feb/25

Find all integer solutions of

3^{m} = 2 n^{2} + 1 .

I o n l y f o u n d m = 1, 2, 5 b y c o m p u t e r

f r o m m = 1 t o m = 30000 .

I s t h e r e a n y g r e a t e r s o l u t i o n s ?

Commented by Rasheed.Sindhi last updated on 10/Feb/25

A l s o m = 0

Commented by Rasheed.Sindhi last updated on 12/Feb/25

D e e p S e e k a s s u r e s t h a t t h e r e i s

n o o t h e r s o l u t i o n f o r m > 5

F i n a l A n s w e r :

(0, 0), (1, \pm 1), (2, \pm 2), (5, \pm 11)

Commented by CrispyXYZ last updated on 12/Feb/25

O k a y t h a n k s . A c t u a l l y I w a s s e e k i n g

p r o o f m e t h o d s .

Commented by ArshadS last updated on 12/Feb/25

d e e p s e e k a l s o c a n h e l p i n t h i s c o n n e c t i o n .

Facebook Tweet Pin