28 November, 2018:
 There can not be three consecutive triangular numbers which can form a Pythagorean triple.
17 December, 2017:
 270 is the smallest positive integer such that it has divisors ending with every decimal digit i.e. divisors ending in 0,1,2,3,4,5,6,7,8 and 9.
30 October, 2016:
 1/37 = 0.027027027...
1/27 = 0.037037037...
(Comments by Al Zimmermann dt 04052017 )
The decimal expansions for 1/27 and 1/37 are as shown above because 27 × 37 = 999.
Another example would be:
1/271 = .00369 00369 00369 …
1/369 = .00271 00271 00271 …
because 271 × 369 = 99999.
4 November, 2015:
 There can not be four triangular numbers in arithmetical
progression.
7 July, 2015:
 54199^{3} = 159211275242599 and 15921 + 12752 + 42599 = 71272
71272^{3} = 362040234715648 and 36204 + 02347 + 15648 = 54199
6 October, 2014:
 48 = 8^{2}  4^{2}
484848 = 848^{2}  484^{2}
4848484848 = 84848^{2}  48484^{2}
48484848484848 = 8484848^{2}  4848484^{2}and so on.
25 December, 2013:
 There are 153 days in any five consecutive months not containing February.
15 July, 2013:
 It is impossible to construct a triangle with sides as distinct Fibonacci numbers
13 November, 2012:
 The smallest perfect number 6 = 1 x 2 x 3
The smallest multiply perfect number 120 = 4 x 5 x 6
The SUM of smallest pair of AMICABLE numbers 220 + 284 = 504 = 7 x 8 x 9
6 February, 2011:
 The smallest integer n such that n/2 is perfect square, n/3 is perfect cube and n/5 is perfect fifth power is 30233088000000.
26 January, 2010:
 The number of letters in ODD, EVEN, PRIME and COMPOSITE are odd, even, prime and composite respectively.
10 May, 2009:
 Every even number greater than 46 can be expressed as sum of two abundant numbers.
18 January, 2009:

639172 is the largest integer with distinct digits whose square consists of digits not included in itself i.e. 639172² = 408,540,845,584
30 December, 2007:
 The Golden Ratio (Phi=1.61803...) can be expressed using four 4's as (√ 4 + √ (4!4) )/4.
14 July, 2007:
 1, 6 and 120 are the only numbers which are both triangular and factorial.
26 January, 2007:
 8589934592 x 116415321826934814453125 (No zero in both numbers)
= 1000000000000000000000000000000000
This is the largest known example of this kind.
25 October, 2006:

The fraction 1/998999 contains Fibonacci numbers
i.e.
1/998999=0.000001001002003005008013021034055089..
(Comments by Al Zimmermann dt 01052017 )
This fraction contains Fibonacci numbers up to 3 digits in length.
This can be generalized as follows::
The fraction 1/(10^2n10^n1) contains Fibonacci numbers up to n digits in length.
If n = 3, the fraction is 1 / (1000000 – 1000 – 1) = 1/998999.
For n = 4, the fraction is 1/99989999 = .0000000100010002000300050008001300210034005500890144….
The n leading zeroes in the decimal expansion can be considered the 0th term in the Fibonacci series or they can be removed by changing the fractions numerator to 10^n:
10000/99989999 = .000100010002000300050008001300210034005500890144….
15 January, 2006:
 The product of 4 consecutive natural numbers can not be a cube.
7 November, 2005:
 A multidigit number with all its digits odd can never be a perfect square.
1 May, 2005:
 27, 58 and 85 are three consecutive Smith numbers and 27 + 58 = 85 .
11 March, 2005:
 The number 3435 is the number such that 3435 = 3^3 +4^4 + 3^3 + 5^5 .
1 January, 2005:
 The number 3608528850368400786036725 is the largest number such that the number formed from first n digits is divisible by n.
15 September, 2004:
 The number FORTY is the only number in English language, all letters of which are in alphabetical order.
4 May, 2004:

The n^{th} fibonacci number F_{n} is divisible by 9, if and only if, n and F_{n} both are even.
2 March, 2004:
 The product of all divisors of a number n is sqrt(n^d), where d is no. of divisors of n.
1 February, 2004:
 The only number which is equal to the sum of subfactorial of its digits is 148349. (i.e. 148349 = !1+!4+!8+!3+!4+!9).
1 January, 2004:
 The only known pair of Twin Pseudoprimes(base2) is 4369 and 4371.
8 November, 2003:
 Every Carmichael number is squarefree.
3 August, 2003:
 No Fibonacci number is equal to the product of two smaller Fibonacci numbers.
13 June, 2003:

1 and 6 are the only triangular Numbers whose squares are also triangular numbers.
21 May, 2003:
 Every number greater than 11 is the sum of two composite numbers.
29 March, 2003:
 8549176320 is a curious number(containing all ten digits) whose digits are in alphabetical order.
1 March, 2003:
 In decimal system 6661661161 is the largest known square with two distinct nonzero digits.
1 February, 2003:
 10662526601 is the only known palindromic cube such that its cube root (i.e. 2201) is nonpalindromic.
1 January, 2003:
 8114118 is the smallest multidigit palindrome such that 8114118^{th} prime i.e. 143787341 is also palindrome.
1 December, 2002:
 Two consecutive numbers i.e. n and n+1 are always relatively prime.
11 November, 2002:

The largest Triangular Number which is the product of three consecutive numbers is 258474216.
5 October, 2002:
 All Semiprimes are deficient numbers.
21 September, 2002:

The smallest Fibonacci number containing all digits from 0 to 9 is F_{74} i.e. 1304969544928657.
6 September, 2002:

Triangular numbers can never end in 2,4,7 or 9.
14 April, 2002:
 The digit in the tens place of a power of 7 is always 0 or
4.
10 March, 2002:
 All Composite Mersenne numbers are Strong Pseudoprimes
(base2).
10 February, 2002:
 There can be maximum five consecutive deficient Numbers and
smallest such set is 7, 8, 9, 10 and 11.
20 January, 2002:
 There can not be four perfect squares in arithmetical
progression.
6 January, 2002:
 The smallest triplet of consecutive Abundant Numbers is
171078830, 171078831, 171078832.
31 December, 2001:
 The largest known Fibonacci Number consisting of only odd
digits is 17711.
23 December, 2001:
17 December, 2001:
 The smallest Fibonacci Number that is also a Smith Number is
1346269.
9 December, 2001:
 The numbers in the series 1, 11, 111, 1111, 11111, ... are
all Triangular Numbers in base9.
30 November, 2001:
 The smallest titanic factorial is 450! . This has 1001 digits and is also known as Arabian Nights Factorial.

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