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Properties and Facts about 2018

The new year has come upon us, and with it a new number to work with. Because of this, I want to compile a list of properties and facts about the number 2018 for use in competitions and problem writing. This can include relationships with other numbers, ways to formulate it as an expression, and expressions involving it; however, any fact about 2018 that could be used in a competition setting can belong here.

I'll start this list off with some basic facts:

  • 2018 is even.
  • The prime factorization of 2018 is \(2 \times 1009.\)
  • 2018 has four digits.
  • The sum of the digits of 2018 is 11.
  • etc. etc. etc.

Feel free to contribute anything about the number 2018 in the comments!

Note by Steven Yuan
2 weeks, 2 days ago

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2018 can be written as a sum of 4 consecutive positive integers, but not as a sum of any other number of consecutive positive integers. This sum is \(503+504+505+506 = 2018\).

Will Van Noordt - 2 weeks ago

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2018 is the sum of 4 distinct nonzero fourth powers:

2^4 + 3^4 + 5^4 + 6^4

Mike Lust - 1 week, 5 days ago

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2018 is the number of ways we can partition 60 into prime parts

here are the first 10 partitions of 60 into prime parts:
{53,7},{53,5,2},{53,3,2,2},{47,13},{47,11,2},{47,7,3,3},{47,7,2,2,2},{47,5,5,3},{47,5,3,3,2},{47,5,2,2,2,2}...

Mike Lust - 1 week, 5 days ago

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good solution

Ayush Jain - 2 days, 8 hours ago

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  • The first digit of 2018 is prime.

  • 2018 has 4 positive divisors.

  • Sum of the 4 positive divisor of 2018 is 3030.

  • 2018 is one larger than a prime number.

  • 2018 can be expressed as the sum of two perfect squares. \(13^2+43^2 = 2018\)

Etc...

Munem Sahariar - 2 weeks, 1 day ago

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Comment deleted 1 week ago

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Its a typo. Thanks

Munem Sahariar - 1 week, 6 days ago

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*2018 in binary= 11111100010 in base of 2

*Divisors = 1, 2, 1009, 2018

*Count from 1 upto 2018 take 33 minute.

*2018 is a deficient number, because the sum of its proper divisors (1012) is less than itself. Its deficiency is 1006.

*2018 is a UnLucky number.

*2018 is a UnHappy number.

Matin Naseri - 2 weeks, 1 day ago

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There are two ways to formulate it as the sum of the difference of two sets of consecutive cubes.

(9^3-8^3) + (25^3 - 24^3)

8&9 are consecutive, 24&25 are consecutive.

and

(15^3-14^3) + (22^3 - 21^3)

Greg Whiteside - 1 week, 1 day ago

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2018 is a Squarefree composite number such that the sum of its divisors is also Squarefree

Mike Lust - 1 week, 5 days ago

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Indeed. I wrote a little problem about this property: it is quite "rare" among all year numbers.

Romain Bouchard - 1 week, 4 days ago

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\(2018\) can be written as a sum 2 perfect squares of which the first digit is perfect square (\(1^2, 2^2\)) repectively and the last digit is both \(3\) : \(2018=13^2+43^2.\)

Pepper Mint - 4 days, 22 hours ago

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