MATH 355 Final: MATH 355 Amherst S17M355 2801 29FinalCox

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 355
• Professor: All

Document Summary

Math 250 take-home final exam due thursday, may 14 at noon. There are seven questions for a total of 100 points plus 10 points of extra credit: (15+5 points) (see exercise 27. 2, pp. Ned by factoring n into a product of primes, n = p1 k1p2 k2 pt kt, and then setting. (d) = (d1)+ (d2)+ + (dr), where d1, d2, . Compute the value of g(n) for all 1 n 18. (d) use your computations in (c), to make a conjecture as to the value of g(n). (e) (extra credit 5 pts. ) Prove that you conjecture in (d) is correct: (15 points) (see exercise 30. 1, p. 234, and the hint there. ) Show that the equation y2 = x3 + xz4 has no solutions in nonzero integers: (10 points) (based on exercise 41. 5, pp. E(q) on the elliptic curve e de ned by the equation. E : y2 = x3 3x + 7. (a) let p = (2, 3) e(q).