MATH 250 Final: MATH 250 Amherst F10M24Final

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 250
• Professor: All

Document Summary

Prove that 11|n if and only if 11| a+b c+d. Hint: think modulo 11: give some examples to illustrate how part a works, now let n be a ve-digit number. State and prove a criterion similar to part a for when 11|n. In 1536, hudalrichus regius discovered that 211 1 = 23 89 and that 213 1 = 8191 is prime. By euclid, the latter implies that 212(213 1) = 33440336. In 1603, the italian mathematician pietro cataldi made a table of is a perfect number. primes < 750 and showed that 217 1 is prime (which he could do using his table since. This gives the perfect number 216(217 1) = 8589869056. Cataldi also claimed that 2p 1(2p 1) is a perfect number for several other exponents, including p = 37. In a 1640 letter to mersenne, fermat showed that cataldi"s claim for p = 37 is wrong by factoring 237 1.