(adsbygoogle = window.adsbygoogle || []).push({}); Randomly select eight odd integers of less than 1000

a) Determine the remainders when dividing their squares by four, and tabualte your results

b) Make a conjecture about your findings

c) test your conjecture with at least five larger integers

d) Prove of justify the conjecture you make.

n tn = n^2 / 4 - 1, Remainder

49 600 1

81 1640 1

121 3660 1

225 12656 1

441 48620 1

625 97656 1

841 176820 1

-----------------------------------------

2001 1001000 1

3673 3372732 1

6925 11988906 1

8123 16495782 1

9999 249950000 1

b) When the square of an odd integer, for n is equal to or greater than 1, is divided by four the result is an even integer with a remainder of 1.

c)

You know that tn = n^2 / 4 - 1, by hypothesis

Factoring n, tn = (n x n)/4 -1

I'm not quite sure where to take my proof from here. Could someone give me a nudge in the right direction?

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# Homework Help: Determine the remainders when dividing their squares by four

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