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Mathematische Nachrichten > 290 > 2-3 > 341 - 348
We present existence theorems for coupled system of quadratic integral equations of generalized Chandrasekhar type which has numerous application (cf. [], [], [] and []). Also, the asymptotic stability of solutions will be considered.
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In 1988, the International Mathematical Olympiad (IMO) was held in Canberra and on day II the following Problem 6 was posed (see [1,2]): Let a and b be positive integers such that ab + 1 divides a 2 + b 2. Show that (a 2 + b 2)/(ab + 1) is the square of an integer.
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Acta Mathematica Hungarica > 2016 > 148 > 2 > 312-327
We prove that if $${\{k, 4k + 4, 9k + 6, d\}}$$ { k , 4 k + 4 , 9 k + 6 , d } , where $${k \in \mathbb{Z}[i]}$$ k ∈ Z [ i ] , $${k \neq 0, -1}$$ k ≠ 0 , - 1 , is a Diophantine quadruple in the ring of Gaussian integers, then $$d = 144k^3 + 240k^2 + 124k + 20.$$ d = 144 k 3 + 240 k 2 + 124 k + 20 .
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Acta Mathematica Scientia > 2011 > 31 > 3 > 1179-1188
In this paper, we give a lower bound exp(2.2 × 10 8 ) for those discriminants of real quadratic fields Q ( d ) with d = N 2 − 4 and h(d) = 1.
