5. Is the number $2020 \cdot 2024-21$ prime or composite? Explain!

## Tasks worth 10 points:
First solution.

$2020 \cdot 2024-21$

$=(2022-2) \cdot(2022+2)-21 \quad 1$ POINT

$=2022^{2}-2^{2}-21$

$1$ POINT

$=2022^{2}-4-21$

$=2022^{2}-25$

$1$ POINT

$=2022^{2}-5^{2}$

$=(2022-5) \cdot(2022+5)$

$1$ POINT

$=2017 \cdot 2027$

1 POINT

The initial number is composite.

1 POINT

TOTAL 6 POINTS

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