Did you know : PRAMIYA* NUMBER

Did you know : PRAMIYA* NUMBER

o  If (P-1) ! + 1 mod P^2 =0   , where P is a prime, then P is a PRAMIYA* NUMBER , PRAMIYA NUMBERS are 5 & 13

Now check ExteMia**

o  In the prime factorization of (P-1)! +1 we will get prime with single power except P=5 or 13 (where P = Prime) 22! + 1 = 23*Q*R*... 

USES :  

o  Total number of factors N! + 1 is in the form of  , except 4!+1 & 12!+1

o  Total number of factors of P! + P are divisible by 3 but not by 9 (due to  in prime factorization), where P is prime except PRAMIYA NUMBER (5 & 13) which is divisible by 4 due to P^3 in prime factorization)

*PRIME + AMIYA **Extension by Amiya

Did You Know

For Maths Lover: THE PALINDROME Calculation

Learn a number and a word (Two In One)

► 264 is the largest number whose square is 'UNDULATING' (6-9-6-9-6)

264^2 = 69696

► UNDULATING


✎ Move with a smooth wavelike motion: "her body undulated to the thumping rhythm of the music".


✎ Have a wavy form or outline: "delightful views over undulating countryside".

Did you know

123475869 is smallest number divisible by 99 which has all digits from 1-9.

Printer's Error Number or Typo-Error Number

Did you know this or heard anywhere :

Printer's Error Number or Typo-Error Number :

Generally we do lot of mistakes in typing, even maths do this too but correct itself. 

Printer's Error Number or Typo-Error Number are number even if you error in typing you would get same value... INTERESTING :)

In this generally we add exponential(power) and multiplication function in between digits (LHS=>RHS in example) or forget to raise power and put multiplications sign (RHS=>LHS in example)

e.g. 

34425 = 3^4*425 
312325 = 31^2*325
492205 = 49^2*205

There are many more.

Thanks Ms. Yashita Jha for sharing smallest such number in decimal base.

To check her number : https://www.facebook.com/MathsByAmiya/posts/528026533916134

Did You Know

► 121 is the only square known of the form 1+p+p^2+p^3+p^4, where p is prime.

121 = 11^2 = 3^0 + 3^1 + 3^2 + 3^3 + 3^4

Another Interesting Series

8 x 8 + 13 = 77
88 x 8 + 13 = 717
888 x 8 + 13 = 7117
8888 x 8 + 13 = 71117
88888 x 8 + 13 = 711117
888888 x 8 + 13 = 7111117
8888888 x 8 + 13 = 71111117
......................... and so on



Note:
(88888......)*8  + 13 = 711....1117

If numbers of 8s in bracket of LHS is "n" then number of 1s in RHS is (n-1)

You might get a question in your examination

(888........is a 101 digits number)*8 + 13 = N
then, what would be sum of digits of N?

Ans: 114

Sol: Since there are 101 8s in LHS so there should in 100 1s in RHS sandwiched between two 7s.

So, total digit sum = 7 + 100*1 + 7 = 114

Did you know

► Last two digits of 76^n are 76 (where n is a natural number).

► If last two digits of ab^n = ab then ab = 00, 01, 25 or 76.

---------------------------------------------------
In your examination, you might get a question :

Find the last two digits of 2345678765676^76876545434^5467876^876567 .

Ans is 76 (since last two digits of base is 76, hardly 2 sec.)

General concept of Last Digit

How to find last digit of A^B

Step I : Find B mod 4* (or remainder by 4*) [say R=0**,1,2,3]

Step II : Write the last digit of base [say L]

Step III: Solve L^R 

[**Note: If R=0, put R=4 instead of 0, or For Odd base direct answer is 1, and for even it's 6]

Step IV : The last digit of L^R is your required last digit.

e.g : Find the last digit of 1234567^55555555

Step I : 55555555 mod 4 = 3 [easy just check for last two digits]

Step II: 7

Step III : 7^3 =343

Step IV : Required Answer = 3

*Last digit is nothing but remainder by 10. The cyclicity of 10 is 4

Fact About 50

Did You Know :

► Half Century (Number 50) is the smallest number that can be written as the sum of 2 squares in 2 distinct ways.

1^2 + 7^2=50

5^2 + 5^2=50

Facts About 43 :

Facts About 43 :
► 43 is the smallest non-palindromic prime which on subtracting its reverse gives a perfect square: 43 - 34 = 3^2

► 43^(7/23) = 3.141539853... (a real accurate approximation of pi)

► 43 + 4^3 is prime.

► IMPORTANT FOR CAT-2013 : Let a(0) = a(1) = 1, and thenceforth

a(n) = (a(0)^2 + a(1)^2 + ... + a(n-1)^2) / (n-1).

Amazingly, a(43) is the first term of this sequence that is not an integer.

Facts About Number 41

► n^2 - n + 41 produces prime numbers for all integers n, from n=0 to n=40 

► The number figures in the polynomial f(n) = n^2 + n + 41, which yields primes for −40 ≤ n < 40.

► 41 is the first number of a prime number sequence that is 41 numbers long:
41 + 2 = 43
43 + 4 = 47
47 + 6 = 53
53 + 8 = 61
61 + 10 = 71
71 + 12 = 83, and so on...

► 41 is the smallest non-palindromic prime which on subtracting its reverse gives a perfect cube (41 - 14 = 3^3), and is also the smallest number that is not of the form |2^x - 3^y|.

Last Term Left

Q.  If 135791357913579......... is a 1000 terms series. If A student of 3E Learning removes odd placed term and creates a new series and repeats the same process again and again and removed all the terms by this process  . What would be the last term removed by him.

Facts About 37

If a 3-digit number of the form "ABC" is a multiple of 37, then so are numbers "BCA" and "CAB" :

37 x  1  = 037

37 x 10 = 370

37 x 19 = 703

37 x  2  = 074

37 x 11 = 407

37 x 20 = 740

37 x  4  = 148

37 x 13 = 481

37 x 22 = 814

37 x  5  = 185

37 x 14 = 518

37 x 23 = 851

37 x  7  = 259

37 x 16 = 592

37 x 25 = 925

37 x  8  = 296

37 x 17 = 629

37 x 26 = 962

'Normal' human body temperature is approx. 37 degrees Celsius.