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Sum of two squares inquiry

Inquiry Maths

A prime number can be expressed as the sum of two squares.

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Inquiry prompt

Inquiry Maths

A prime number can be expressed as the sum of two squares.

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Inquiry prompt

Inquiry Maths

A prime number can be expressed as the sum of two squares.

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Link to the Regulatory Cards

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Alternative prompts

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Inquiry prompt

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Inquiry prompt

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Lines of inquiry

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1. Explore prime numbers.

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2. Explore composite numbers.

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The numbers as the product of prime factors.

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3. Express a positive integer as a sum of square numbers in two ways.

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These are the first three numbers that can be expressed as the sum of two squares in two ways.

What do you notice?

Extend the list by using prime factors.

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4. How many ways can you express a positive integer as the sum of squares? How do you find the different ways?

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If we use positive integers only and ignore the order, then there are four distinct ways:

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Another example: 650 expressed as the sum of two squares.

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5. Find positive integers that can be expressed as two squares using complex numbers.

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6. Express positive integers as the sum of two or more cubes.

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Independent inquiry

Identify patterns in the positive integers that can be expressed as the sum of two cubes.

Carry out research into how to determine if a number can be expressed in this way.

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