Families of Even Non-congruent Numbers with Odd Prime Factors of the Form 8k+5

초록

A positive integer is called a congruent number if it is equal to the area of a right triangle having all side lengths rational. In this paper, we find new families of non-congruent numbers whose odd prime factors are all congruent to 5 modulo 8. To obtain our results, we make use of the Monsky matrix with the aid of graph theory.

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