The Girl Who Loved Math - Melanie Wood is only female to represent US in International Mathematical Olympiad

When the dickering finally ends, Russia and China have tied for first. Romania is fourth, and the United States places ninth. Nevertheless, Reid Barton and Paul Valiant win gold medals; Gabriel Carroll, Po-Shen Loh, and Melanie get silver; and Lawrence Detlor is awarded a bronze. Characteristically, Melanie is not rocked by the loss. "As a team, we certainly didn't do better than average for the United States," she says. "Still, all the teams that placed above us are very good."

Coach Andreescu reassures his charges: "The coordinator congratulated me for the thoroughness of your solutions. Even though they were not the simplest, they showed mathematical maturity that impressed him." Later he adds, "That test would have been a challenge for a professional mathematician."

A PROFESSIONAL MATHEMATICIAN IS WHAT MELANIE PLANS TO be, although she just might "end up directing on Broadway," because she is majoring in theater as well as math. She has finished her freshman year at Duke University, which she chose over Harvard because she thought the math department there was "cold and competitive." She has been taking graduate-level classes in real analysis, complex analysis, and algebraic number theory, along with a drama class entitled Voice and Body Gesture.

This month Melanie is working with the U.S. math team's summer program as a grader, which gives her a chance to mentor younger mathematicians bound for next month's Olympiad in Seoul. All through high school she volunteered at MathCounts, the middle-school competition in which she had competed. "One of my jobs was emceeing the Cool Down Round, which follows the official competition. I run around with a mike among students who are furiously solving problems, and I jump on tables, yelling, `Hey, hey, we have an answer over here.' It's nothing like an actual math competition. Competitions are silent. Most of the math I do isn't competition math. It's openly working with others and full of laughter." Like her father, Melanie is passing along her love of mathematics to others in an exuberant, generous way that no doubt would have made him proud.

SATISFYING PAIRS

This was one of six problems contestants were asked to solve at the International Mathematical Olympiad in Bucharest last year. This year's Olympiad will be held in Seoul, South Korea, on July 18 and 19.

Find all pairs (n,p) of positive integers such that

* p is prime

* n [is less than or equal to] 2p

* [(p-1).sup.1] + 1 is divisible by [n.sup.p-1]

Hint: The cases P|n and p/n should be handled separately, In the latter case, consider the congruence [(p-1).sup.n] [equivalent] -1 modulo a suitable prime divisor of n.

MATH OLYMPICS SOLUTIONS

The pairs satisfying the given condition are (n,p) = (1,p) for any prime p, (2,2) and (3,3). The reader may easily check that these actually are solutions, and that there are no more solutions for p = 2, 3. So we may assume hereafter p [is greater than or equal to] 5 and n [is greater than or equal to] 2. In particular, since [(p - 1).sup.n] + 1 is odd and n divides this quantity, n must be odd.