关于二元线性方程的正整数解的个数
On the Number of Positive Integer SOlutions of Binary Linear Equations
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摘要: 设a,b,c,k是适合gcd(a, b)=1的正整数.证明了：恰有ab个不同的正整数c可使方程ax+by=c共有k组正整数解(x, y)，而且c的最大值和最小值分别是ab(k+1)和ab(k-1)+a+b.Abstract: Let a,b,c,k be positive integers with ged(a, b)=1.It is proved that there exist exactly ab distinct c which make the equation ax+by=c to have k positive integer solutions (x,y).Moreover,the maximum and the mnimum of c are ab(k+1) and ab(k-1)+a+b respectively.
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Key words:
- binary linear equations /
- postive integer solutions /
- number of solutions .
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