Problem 97 Let A be any set of 51 distinct integers chosen from 1, 2, 3,., 100. Prove that there must be two distinct integers in A such that one divides the other. Problem 98 Given a positive integer n, show that there exists a positive integer containing only the digits 0 and 1 (in decimal notation), and which is divisible by n.
Problem 97 Let A be any set of 51 distinct integers chosen from 1, 2, 3,., 100. Prove that there must be two distinct integers in A such that one divides the other. Problem 98 Given a positive integer n, show that there exists a positive integer containing only the digits 0 and 1 (in decimal notation), and which is divisible by n.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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plz solve the problem 97 with explanation i will give you upvote.
Transcribed Image Text:Problem 93 Mr. and Mrs. Smith went to a party attended by 15 other couples. Various
handshakes took place during the party. In the end, Mrs. Smith asked each person at the party
how many handshakes did they have. To her surprise, each person gave a different answer. How
many hand shakes did Mr. Smith have? (Here we assume that no person shakes hand with his/her
spouse and of course, himself/herself.)
Problem 94 Suppose that a + 1/a E Q. Prove that an + 1/an E Q for all integer n> 0. Problem 95
Suppose that the sequence of integers {an} satisfies a0 = 0, al = a2 = 1, an+1
(-1)n. Prove that an is a perfect square.
3an + an-1 2=
Problem 96 24 chairs are evenly spaced around a circular table on which are name cards for 24
guests. The guests failed to notice these cards until they have sat down, and it turns out that no
one is sitting in fornt of his/her own card. Prove that the table can be rotated so that at least two
of these guests are simultaneously correctly seated. (A much harder questions is: Can the table be
rotated so that at least 3 guests are simultaneously seated correctly?)
Problem 97 Let A be any set of 51 distinct integers chosen from 1, 2, 3,..., 100. Prove that there
must be two distinct integers in A such that one divides the other. Problem 98 Given a positive
integer n, show that there exists a positive integer containing only the digits 0 and 1 (in decimal
notation), and which is divisible by n.
Please don't give incomplete answers.
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