Question: I need help with proof. Prove: If n is a positive integer such that n mod 4 (the remainder of n under division by 4)

I need help with proof.

Prove: If n is a positive integer such that n mod 4 (the remainder of n under division by 4) is 2 or 3, then n is not a perfect square. [8, pretty difficult]

Hints: Use contraposition! Knowing n = k², check the values of k mod 4 (there are 4: 0, 1, 2 and 3) and find out what that says about the remainders of n.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Proof 5.1: Prove (") ("?" k) = (") (" ) with k +lyn. Proof 5.2: Let n be a positive integer. Show that (27 ) + (2n) = 1(2n+2) Proof 5.3: Prove 1 1 n + + J ... 1 .4 4 .' 7 . 10 (3n - 2) (3n + 1) 3n + 1

Observe that mod and div can be defined as functions from Z n o n n e g Z + to Z . For each ordered pair ( n , d ) consisting of a nonnegative integer n and a positive integer d , let the nonnegative...

Instructions The following five sections; Direct proof Proof by contrapositive Proof by contradiction Proof with cases Proof of a biconditional Two proofs in each section from the proposed exercises....

\fCPSC 121: Models of Computation Assignment #4, due Wednesday, November 18th , 2015 at 17:00 Each of the following questions asks you to prove a theorem. When the theorem is stated in English, it...

Prove this modular arithmetic property: [(a mod n) * (b mod n)] mod n = (a * b) mod n; where a and b are integers, n is a positive integer, and * is the multiplication operation. Hint: one way is to...

3 ,,uoh "gram 3 Eww 3 m T mm H a 3 .2 ' m w .,.m.av>v 3. m. @3on we geonwoaoa mm H "with M'nr H E. wads + we A at. ES 0 3.8V WEE 3563 mo wow 23 E m \"9H .3 avgmeMm\" mnemagouom Aggy\"...

MUST BE CORRECT ANSWERS A small software company has the following simplified cashflow, funded by shareholders' equity of 20,000 and a bank overdraft of 5000: Invoiced money received 2 months after...

A seismic probe bores itself into the seabed, going as deep as it can before running out of fuel. This takes about five minutes. It rotates its spiral drill head at rate R(t) that follows a...

That is all the information here. matics? 4 What's True in Mathematics? Theorem 4.1 Let n be a positive integer for which 2" - 1 is a prime number. Then the number 2"- (2" - 1) is a perfect number....

question no3 Exercises 1. There are infinitely many stations on a train route. Sup- pose that the train stops at the first station and suppose f) Explain why these steps show that this formula is...

Calculate the reduced price, if an item costing $19.25 is marked up by 35% of the selling price and then marked down by 25%.

The table to the night shows the number of people, in thousands, in a country without health insurance in a certain year. Complete parts a) through d) below. a) What percentage of the countries...

Which step in calculating the overall reasonableness test for annual depreciation is incorrect a add 1 / 2 of the asset additions be add 1 / 2 of the salvage values see deduct all fully depreciated...

Exercise 3. Consider the open network of two queues shown in Figure 2. Customers enter the network at rgure Li vpen queuenty networ. rate immediately reaching queue 1 . Customers leaving queue 1 will...