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On a Conjecture Concerning the Exponential Diophantine Equation a~x+b~y=c~z

Le Mao - hua (Department of Mathematics,Zhangjiang Normal College,Zhangjinang Guuangdong,524048)  
Let r be an odd integer with r 1, m be an even integer. Let Ur, Vr beintegers satisfying and c was a power of prime, then the equation ax + by = cz had only the positive integer solution (x,y,z) = (2, 2,r).
【Fund】: 国家自然科学基金(10271104);; 广东省自然科学基金(011781);; 广东省教育厅自然科学研究项目(0161);; 湛江市988科技兴湛计划项目
【CateGory Index】: O156
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Chinese Journal Full-text Database 4 Hits
1 YANG Shi-chun (A’Ba Teachers College,Wenchuan,Sichuan,623000,China);On the Solutions of the Exponential Diophantine Equation |m~4-6m~2+1|~x+(4m~3-4m)~y=(m~2+1)~z[J];Guangxi Sciences;2007-01
2 ZHANG Jin-lai(Chaoyang Teachers College,Chaoyang 122000,China);On the Diophantine Equation 31 x~2+33~y=2~z[J];Journal of Jiamusi University(Natural Science Edition);2008-03
3 LE Mao-hua(Department of Mathematics,Zhanjiang Normal College,Zhanjiang 524048,Guangdong China);On the Prime Solutions of the Diophantine Equation X~2+Y~2=Z~r[J];Journal of Jishou University(Natural Sciences Edition);2006-02
4 LE Mao-hua (Department of Mathematics, Zhanjiang Normal College. Zhanjiang 524048, China);On a Conjecture Concerning the Exponential Diophantine Equation a~x+b_y =c_z[J];;2003-06
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