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Shkiper50 [21]
3 years ago
7

Find 5 rational numbers between 1/3 & 2/5​

Mathematics
1 answer:
Alexeev081 [22]3 years ago
3 0

Answer:

41/120, 7/20, 43/120, 11/30, 3/8

Step-by-step explanation:

Write the numbers.

1/3 & 2/5

We need a common denominator, but not the least common denominator. Both 3 and 5 are factors of 60, so let's use 60 as the common denominator.

Multiply 1/3 by 20/20:

1/3 = 20/60

Multiply 2/5 by 12/12:

2/5 = 24/60

Let's multiply each fraction again, but this time by 2/2.

1/3 = 40/120

2/5 = 48/120

Now it's easy to find 5 numbers between 40 and 48, so we get:

41/120, 42/120, 43/120, 44/120, 45/120

Some of these fractions can be reduced, so our answer is:

41/120, 7/20, 43/120, 11/30, 3/8

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Fermat's little theorem states that
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If we divide both sides by a, then
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Rewrite
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and apply Fermat's little theorem
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=>
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So we conclude that
a^{1000000}≡1 mod 17

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