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tamaranim1 [39]
4 years ago
10

Perform the modular arithmetic. (7 · 15) (mod 4)

Mathematics
1 answer:
Reika [66]4 years ago
4 0

We could do it by first writing

7\cdot15=(4+3)\cdot(4+11)=4^2+14\cdot4+33

so that

7\cdot15\equiv4^2+14\cdot4+33\equiv33\pmod4

and since 33=32+1=8\cdot4+1, we have

7\cdot15\equiv33\equiv1\pmod4

# # #

Alternatively, we can just compute the product and take it mod 4:

7\cdot15=105=104+1=26\cdot4+1

and so we get the same result of 1.

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