Question: What is the smallest positive integer that can be expressed as the sum of two cubes in two different ways?

The number 1729 can be expressed as the sum of two cubes in two distinct ways: 1729 = 1^3 + 12^3 = 9^3 + 10^3. This interesting mathematical result is known as the Hardy-Ramanujan number. The discovery of this special property was made by the renowned mathematician Srinivasa Ramanujan, who visited his mentor, G.H. Hardy, when he was ill. To lighten the mood, Hardy mentioned that the cab he traveled in, numbered 1729, was rather dull. Ramanujan quickly replied that it was, without a doubt, a fascinating number as it could be expressed as the sum of two cubes in two distinct ways! This unexpected mathematical encounter highlights the beauty and intriguing nature of numbers.

Math question: The number 1729 can be expressed as the sum of two perfect cubes. Find the two cubes and their sum.

Consider the equation a³ + b³ = 1729, where a and b are positive integers. By trial and error, we find that a = 10 and b = 9 are the values that satisfy the equation. Thus, 10³ + 9³ = 1000 + 729 = 1729, meaning that 1729 is the sum of the cubes of 10 and 9.

Math question: If a number is divisible by 13, 7, and 11, and when divided by 9 leaves a remainder of 1, what is the number?

To find the number, we need to consider the least common multiple (LCM) of 13, 7, and 11, which is 1001. Adding multiples of 1001 to the remainder 1, we find that the number must be of the form 1001n + 1. Now, we need to find the smallest n for which 1001n + 1 is divisible by 9. By trying successive values of n, we find that n = 1729 satisfies the condition. Hence, the number is 1001 * 1729 + 1 = 1,731,730 + 1 = 1,731,731.

Max	9223372036854775807
25835	Positive integer
0b10001100	Binary number
01771452	Octal number
0x129abf	Hex number
5.012 * 10^7	Scientific notation
2^4 * 5	Factorized form
*	Random number

1729 (number)

1729 is an odd 4-digits composite number following 1728 and preceding 1730. In scientific notation, it is written as 1.729 × 10^3. The sum of its digits is 19. It has a total of 2 prime factors and 4 positive divisors. There are 1296 positive integers (up to 1729) that are relatively prime to 1729.

Interesting facts

1729 has 4 divisors, whose sum is 1840
The reverse of 1729 is 9271
Previous prime number is 91

Basic properties

Is Prime? no
Number parity odd
Number length 4
Sum of Digits 19
Digital Root 1

Name

Name	one thousand seven hundred twenty-nine

Notation

Scientific notation	1.729 × 10^3
Engineering notation	1.729 × 10^3

Prime Factorization of 1729

Prime Factorization 91 × 19

Composite number

ω	Distinct Factors	2	Total number of distinct prime factors
Ω	Total Factors	2	Total number of prime factors
rad	Radical	1729	Product of the distinct prime numbers

The prime factorization of 1729 is 91 × 19. Since it has a total of 2 prime factors.

Most popular turbo-numbers

9, 7, 81, 88, 19, 307, 1201, 2060, 84166, 53257, 550228, 51147, 7411273, 5691044, 17735362, 65930284, 43446195, 872096786, 6321863767, 145311994

Basic calculations (n = 1729)

Multiplication

n×y

n×2	3458
n×3	5187
n×4	6916
n×5	8645

Division

n÷y

n÷2	864.5
n÷3	576.33333333333
n÷3	432.25
n÷5	345.8

Exponentiation

n^y

n²	2989441
n³	5168743489
n⁴	8936757492481
n⁵	15451653704499649

Nth Root

^y√n

²√n	41.581245772584
³√n	12.002314368428
⁴√n	6.4483521749811
⁵√n	4.4417999886365

Divisors of 1729

1, 19, 91, 1729

4 divisors

τ	Total Divisors	4	Total number of the positive divisors of n
σ	Sum of Divisors	1	Sum of all the positive divisors of n
s	Aliquot Sum	-1728	Sum of the proper positive divisors of n
A	Arithmetic Mean	0.25	Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n))
G	Geometric Mean	1	Returns the nth root of the product of n divisors
H	Harmonic Mean	4	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 1729 can be divided by 4 positive divisors. The sum of these divisors (counting 1729) is 1, the average is 0.25.

Base conversion 1729

Base	System	Value
2	Binary	11011000001
3	Ternary	2101001
4	Quaternary	123001
5	Quinary	23404
6	Senary	12001
8	Octal	3301
10	Decimal	1729
12	Duodecimal	1001
16	Hexadecimal	6c1
20	Vigesimal	469
36	Base36	1c1

Cryptographic Hash Functions

md5	25e2a30f44898b9f3e978b1786dcd85c
sha1	7dbb8092234523ada33338f67beff47874ef27fb
sha256	98b1690510df1bf21fe13018a2641b19c7f3871f289b523b395d0bffa3574be9
sha512	ba5a3c46a378914bc59d5da379a922102953bf6830cbddf0e4b295a89d5bd668dd4bf88e62ad2fc023f34bdf56e2265a254b5291381f675dba9df9a649850c6f
ripemd-160	f5c606b68e04ae1021e43a50c2d226ca66c98f6d

1729 as geometric shapes

Circle

Radius = n

Diameter	3458
Circumference	10863.627396114
Area	9391605.8839401

Sphere

Radius = n

Volume	21650782097.777
Surface area	37566423.53576
Circumference	10863.627396114

Square

Length = n

Perimeter	6916
Area	2989441
Diagonal	2445.1752493431

Cube

Length = n

Surface area	17936646
Volume	5168743489
Space diagonal	2994.7158462866

Equilateral Triangle

Length = n

Perimeter	5187
Area	1294465.9245574
Altitude	1497.3579231433

Triangular Pyramid

Length = n

Surface area	1294465.9245574
Volume	609142261.88095
Height	815.05841644769