The diophantine problem Y² - X³ = A in a polynomial ring

Let C[z] be the ring of polynomials in z with complex coefficients; we consider the equation Y² — X³ = A, with A[is an element of]C[z] given, and seek solutions of this with X, Y[is an element of]C[z] i.e. we treat the equation as a "polynomial diophantine" problem. We show that when A is of degree 5 or 6 and has no multiple roots, then there are exactly 240 solutions (X, Y) to the problem with deg X ≤ 2 and deg Y ≤ 3

The Relationship of the Self-Concept and the Reflected Ideal Self to Various Components of Friendship

This investigation was designed to examine some of the rela tionships between self-concepts, evaluations by others, and friendship. It was hypothesized that a person who is seen by a second person similarly to the way the first person would like to see himself will be more likely to form friendships with the second person, and more likely to see him as ego supportive than when such similarity does not exist. It was also predicted that people who see themselves as being quite different from the way they would like to be (unfavorable self-concepts) will be more likely to be involved in relationships characterized by strain and discord than will people who see themselves as being similar to the way they would like to be (favorable self-concepts). The subjects reported for the experiment in same-sex pairs who were acquainted. Each partner completed the IAV which measures the subject*s real and ideal selves, and was modified in this exper iment to measure also the concepts of their partners. They also described their partners in terras of the ADF. The subjects wore divided into high and low groups on t\ The first hypothesis was supported with respect to VID, but not with respect to ESV. That is, the low reflected ideal discrepancy subjects assigned significantly higher VID, but not ESV, scores to their partners than did the high reflected ideal discrepancy subjects. All results for the second hypothesis xvere negative. No significant relationships were found between the size of a subject\u27s self-concept discrepancy; and the DTM assigned to his partner, the DTM he was assigned by his partner, or the DTM he assigned his partner plus the DTM his partner assigned to him