1 If p is an even integer and q is an odd integer, then p3 + 2q2 is an even integer.
1 If p is an even integer and q is an odd integer, then p3 + 2q2 is an even integer.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Detailed proof of number 1 please. With the claim and the proof and the conclusion.
Transcribed Image Text:1. If \( p \) is an even integer and \( q \) is an odd integer, then \( p^3 + 2q^2 \) is an even integer.
2. If \( a \) is an odd integer, then \( 16 \mid (a^4 + 4a^2 + 10) \).
3. If the odd natural number \( m \) has the form \( 4k + 1 \) for some integer \( k \), then \( m - 1 \).
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