Problems need HardWork #21
Find the number of pairs of integer solutions :
x 3 + y 4 = 7
The answer is 0.
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1 solution
How do I know which number to take as a modulus to prove the existence of integer solution?
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i f t h e r e i s a e q u a t i o n l i k e x a + y b = k , a n d i f ( a b + 1 ) i s p r i m e y o u s h o u l d t a k e m o d ( a b + 1 )
I didn't understand. What did you mean ny congruence of a power?
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l i k e t a k i n g c u b e s o f n u m b e r s a n d t h e n f i n d i n g w h a t r e m a i n d e r i t g i v e s w h e n d i v i d e d b y 1 3 A n d t h e n s i m i l a r l y f o r t h e f o u r t h p o w e r s
j u s t t a k e m o d 1 3 W h a t a r e t h e c o n g r u e n c e s o f t h i r d p o w e r s ? 0 , 1 5 , 8 , 1 2 W h a t a r e t h e c o n g r u e n c e s o f f o u r t h p o w e r s ? 0 , 1 , 3 , 9 t h e r e i s n o p a i r w h i c h c a n g i v e u s 7 m o d 1 3 H e n c e , t h e r e a r e n o i n t e g r a l s o l u t i o n s t o t h i s e q u a t i o n