1. Prove that if n is an integer and n is a multiple of 2, then 4n+ 24 is a multiple of 8. 2. Show that if a = b (mod m) and b = c (mod m) where a and b are non-zero integers and m is a positive integer, then a = c (mod m). (Recommended start: write the congruences as statements of divisibility, and divisility as equalities, then go from there). ur text videos potes etc pnosted to Discourse. No other outside resources (including humans)
1. Prove that if n is an integer and n is a multiple of 2, then 4n+ 24 is a multiple of 8. 2. Show that if a = b (mod m) and b = c (mod m) where a and b are non-zero integers and m is a positive integer, then a = c (mod m). (Recommended start: write the congruences as statements of divisibility, and divisility as equalities, then go from there). ur text videos potes etc pnosted to Discourse. No other outside resources (including humans)
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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Please follow exactly the solution steps as the one on the 2nd image for a DIFFERENT question. The way you answer my question should follow exactly those steps and procedures
Transcribed Image Text:Learning Target L5 (Core): I can correctly structure a careful mathematical proof including all relevant English
and mathematical statements.
Please remember the academic integrity policy that you swore to uphold. Proofs can be challenging. Just
try your best. If you don't get it this week, you have many more opportunities!
1. Prove that if n is an integer and n is a multiple of 2, then 4n+ 24 is a multiple of 8.
2. Show that if a = b (mod m) and b = c (mod m) where a and b are non-zero integers and m is a
positive integer, then a = c (mod m). (Recommended start: write the congruences as statements of
divisibility, and divisility as equalities, then go from there).
You can use our text, videos, notes etc, posted to Discourse. No other outside resources (including humans)
are allowed.
Transcribed Image Text:LS:
(1) Proof
by
contradiction:
Assume, to the contrary that
So
that
integers
Them
(2) Proof
Assume
an
integer
Consider
Checkpoint 5 Solution....pdf
4(a + 2b) = 57₁
but since 57 isn't divisible by 4, this is impossible!
Thus it must be that
a and b
tv
So
that a and b
4₁+ 8b = 57.
by contraposition.
that
k
50
n² = (k+1)²
= 4k² + 4k+1
= 2(ak² + 2k)+1
2x1².
Thus, if 2 /n², we have nis
E
ni odd. Then there exists
that
n=2k +1.
are
MacBook Air
are not
not integers!
even by contraposition.
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