
3.E Exercises

• Page ID
7526
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Exercise $$\PageIndex{1}$$:

Let $$a, b, c \in \mathbb{Z}$$, such that $$a \equiv b (mod\,n).$$

Show that  $$ac=bc(mod\,n).$$

Exercise $$\PageIndex{2}$$:

Find the remainder, when $$(201)(203)(205)(207)$$  is divided by $$13.$$

Exercise $$\PageIndex{3}$$:

Show that the sum of 2 odd integers is even.

Exercise $$\PageIndex{4}$$:

Given that February 14, 2018, is a Wednesday, what day of the week will February 14, 2090 be?

Exercise $$\PageIndex{5}$$:

Find the remainder when 81789  is divided by 28.

Exercise $$\PageIndex{6}$$:

Find the remainder,

1.  When $$3^{1798}$$ is divided by $$28.$$
2.  When $$2^{1798}$$ is divided by $$28.$$
3.  When $$7^{5453}$$ is divided by $$8.$$

Example $$\PageIndex{7}$$:

Given a positive integer $$x,$$ rearrange its digits to form another integer $$y.$$ Explain why $$x-y$$ is divisible by $$9.$$