Number seventeen

The number seventeen is a natural number before 18, it follows 16. In Roman numerals, it is written XVII.

Summary

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• 1 Properties
  • 1 Arithmetic
  • 2 Severability
  • 3 Notations
  • 4 Geometric
• 2 Sources

Properties

Arithmetic

• 17 is the seventh prime number, after thirteen and before nineteen.
• 17 is the third prime number of Fermat (n = 2), after 5 and before 257. Thanks to this property, heptadecagons with ruler and compass can be built, as Carl Friedrich Gauss demonstrated.
• Make a pair of twin prime numbers along with 19.
• 17 = 13 + 2 + 2 = 11 + 3 + 3 = 7 + 7 + 3
• Since (4 + i) (4-i) = (1 + 4i) (1-4i) = 17, this number is not prime in the ring of Gaussian integers. I don’t know
• 17 is the sum of two squares 4 ²+ 1 ² , since it is a prime of the form 4k + 1 (k, integer), it also divides a sum of squares 9 ² + ^{2 2}
• It is a Pythagorean prime number.
• Since 17 = 9 + 4 + 4, sum of three squares, its square root would be the diagonal of a straight rectangular prism-
• 17 is the sum of three cubes 2 ³+ 2 ³ + 1 ³ = 17
• Sum of two fourth powers 2 ⁴+ 1 ⁴ = 17
• sum of the first four rational primes 2 + 3 + 5 + 7

Divisibility

• Let K = 10a + b, when a + 12b is a multiple of 17, it will be K. ejm, 4182 → 418 + 2×12 = 442 → 44 + 2×12 = 68, multiple of 17

Notations

• base two or binary: 10001
• base 3 or ternary: 122
• base 4, quaternary 101
• base 5, quinary 32
• senario 25
• octal 21
• base 12 duodecimal 15
• base 16 hexadecimal 11

Geometric

• A 17-sided polygon is called the heptadecagon
• By 17 points of the non-aligned plane of three, 17 (17 + 1) can be drawn: 2 = 153 lines
• Gauss wanted a 17-sided polygon (heptadecagon) to appear on his tombstone