Question

(1) Solving systems of congruences. (3 pts each) Solve the following problems, by either the iterative method (method A, as discussed in class), or by using the "closed formula" method (method B discussed in class and on HW 8, problem 7). Do the first two problems by hand. For the third problem you may use a modular arithmetic calculator. Check your results (ii)-3 (5), x 2; (6) Z Ξ 4 (11). , ii) President McRobbie proudly announces that IU has received a large donation of several million dollars (but less than $130M). If it would all be spent on building new residence halls, for $20.507.000 each, $8.479.000 would be left over. If it would all be spent on establishing endowed chairs with an endowment of $5.340.000 each, $580.000 would be left over. If it would all be spent on scholarships for students in the amount of $29.000 each, $23.000 would be left over. How large is the donation? Hint. For (iii), divide al numbers by 1000, then carry out the calculations (and do not forget to multiply eventually again by 1000).

Answer 1

140 354一三 1 (mod 4) 331 Cmed mod t 6X6-36 Elmol 구

330 66-65 Во-22R 892 ) (Mod)! ged ( 1):1.

t (mod ±a 20148 +l10+ 810 x 5go (mod 5340