On The Diophantine Equation(47n)~x+(1104)~y ＝(1105)~z

For odd modern first congruence equationax≡b（modm）,we can get a complete set of residues prime to m through finitely multiplying 2.Therefore having i,such that2ⁱa₁≡1（modm₁）,this equation must have solutions.Let a,b,c be relatively prime positive integers such thata ²+b²=c².In 1956,Jesmanowicz conjecture that for any positive integer n,the only solution of（a n）^x+（b n）^y=（c n）^z in positive integers is（x,y,z）=（2,2,2）.In this paper,we show that（47n）^x+（1104n）^y=（1105n）^z has no solution in positive integers other than（x,y,z）=（2,2,2）.In this paper,we show this conjecture for the case that a or b is 2^r1+1n₁ where r₁,n₁ is any positive integer.