1458_(number) Knowpia

← 1457 1458 1459 →
List of numbers; Integers; ← 0 1k 2k 3k 4k 5k 6k 7k 8k 9k →
Cardinal	One thousand four hundred [and] fifty-eight
Ordinal	1458th; (one thousand four hundred fifty-eighth)
Factorization	2 × 36
Divisors	1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486, 729, 1458
Greek numeral	,ΑΥΝΗ´
Roman numeral	MCDLVIII
Binary	101101100102
Ternary	20000003
Senary	104306
Octal	26628
Duodecimal	A1612
Hexadecimal	5B216

1458 is the integer after 1457 and before 1459.

The maximum determinant of an 11 by 11 matrix of zeroes and ones is 1458.^[1]

1458 is one of three numbers which, when its base 10 digits are added together, produces a sum which, when multiplied by its reversed self, yields the original number:

1 + 4 + 5 + 8 = 18

18 × 81 = 1458

The only other non-trivial numbers with this property are 81 and 1729, as well as the trivial solutions 1 and 0. It was proven by Masahiko Fujiwara. ^[2]

References edit

^ Hadamard, J. (1893), "Résolution d'une question relative aux déterminants", Bulletin des Sciences Mathématiques, 17: 240–246
^ Fujiwara, M. (2005), Introduction to Truly Beautiful Mathematics, pp. 100–101

[1] Hadamard, J. (1893), "Résolution d'une question relative aux déterminants", Bulletin des Sciences Mathématiques, 17: 240–246

[2] Fujiwara, M. (2005), Introduction to Truly Beautiful Mathematics, pp. 100–101

[1]

[2]

Summary

References edit