Numbers 87,000,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

80,000,000 81,000,00082,000,00083,000,000 – 84,000,000

85,000,00086,000,00087,000,00088,000,00089,000,000

All Numbers  & [1M] & [10M- [20M] - [30M] - [40M] - [50M] - [60M] - [70M] - [80M] - [90M]  &  [100M]

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 87,109,375

[Math.]  Its odd powers end with 87,109,375.  Its even powers end with 12,890,625.

 

87,109,376

[Math.]  An automorphic number, whose powers end with the number itself. It is extracted from a 17-digit automorphic number 43,740,081,787,109,376, which remains automorphic when dropping the left-most digits. (References [15])

 

87,128,712 & 8,799,912

[Math.]

(*)   8712 = 2178×4 & 8712×2178 = 18,974,736 = 43562 (= 664)

8712…8712 = 2178…2178×4 & 8712…8712×2178…2178 = 4356…43562.

 

(**)   87912 = 21978×4 & 21978×87912 = 439562

87912…87912 = 21978…21978×4 & 21978…21978×87912…87912 = 43956…439562.

(***)   87999912 = 21999978×4 & 21999978×87999912 = 439999562

87999912…87999912 = 21999978…21999978×4 &

21999978…21999978×87999912…87999912 = 43999956…439999562.

 

(****)   879…912 = 219…978×4 & 219…978×879…912 = 439…9562

879…912…879…912 = 219…978…219…978×4 &

             219...978...219...978×879...912...879...912 = 439...956...439...9562.

 

87,133,365

[Math.]  A pair of amicable numbers (79324875, 87133365).

 

87,354,495

[Math.]  A pair of amicable numbers (74386305, 87354495).

 

87,403,803

[Math.]  The 38th Lucas number.

 

87,539,319

[Math.]  The smallest number that can be expressed as the sum of 2 cube numbers in 3 non-trivial ways: 87,539,319 = 4363+1673 = 4233+2283 = 4143+2553, (Leech, 1957). The next numbers are: 175,959,000 = 5603+703 = 5253+3153 = 5523+1983 (Gerardin, 1908) and 327,763,300 = 3003+6703 = 3393+6613 = 5103+5803.  (Ref.14)

 

87,624,375

[Math.]  87,624,3753 = 672,782,675,854,638,427,734,375; All digits are "triplicated". (References [15])

 

87,654,321

[Math.]  Number 087,654,321 misses one digit 9 in 10 digits 0-9 and so do its multiplies 087,654,321×2 = 175,308,642, 087,654,321×4 = 350,617,284, 087,654,321×5 = 438,271,605, 087,654,321×7 = 613,580,247 and 087,654,321×8 = 701,234,568.

 

87,889,091

[Math.]  A prime number, specially concatenated from 87, 88, hidden prime 89, 90 and 91.

 

87,998,470

[Math.]  A pair of amicable numbers (87998470, 102358010), one of 5 pairs involving an 8-digit and a 9-digit number.

 

8,799,912 & 87,128,712 (see above)

 

xy,abc,def

[Math.]  For any xy = 10 to 99, there are always six 6-digit numbers abc,edf such that the sum (xy+abc,def) is equal to one of 6 digit-rotations of 142,857 and the number xy,abc,def is a multiple of 142,857.

 

For any xy = 10 to 99, there are always twelve 6-digit numbers abc,edf such that the sum (xy+abc,def) is equal to one of 12 digit-rotations of 076,923 or 153,846 and the number xy,abc,def is a multiple of 76,923.