Wonders of Number description

ENJOY THE BEAUTY OF NUMBERS !!!

This app consists of two modes :

1. Multiple Mode :

Given any number n, excluding multiples of 2 or 5, we can find a multiple of n which entirely consists of 1's only.

For example given 3 (neither divisible by 2 nor 5) as input, the output 111 is divisible by 3 (i.e. 111 is a multiple of 3)
and given 7 (neither divisible by 2 nor 5) as input, the output 111111 is divisible by 7.

43 is input and the output is given below :
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111111111111111111111 (21 digits number) which is divisible by 43.

4967 is input and the output is given below :
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1111111...111111 (4966 digits number) which is divisible by 4967.

4943 is input and the output is given below :
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1111111...111111 (4942 digits number) which is divisible by 4943.

6801 is input and the output is given below :
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1111111...111111 (3399 digits number) which is divisible by 6801.


*** WARNING :
For some numbers, mobile devices may hang as it might take huge time for computation.

In this mode n can be entered as input and the app will give the proper multiple of n satisfying the above mentioned condition.

App will take input between 2 to 10000.

*** WARNING :
For some numbers, it may return no result.

2. Sum Mode :

Any integer number n can be expressed as

n = (+/-)1^2(+/-)2^2(+/-)3^2(+/-) .... (+/-)N^2

Here (+/-) means either + or - and N is an integer.

For example :

2 = -(1^2+2^2+3^2)+4^2

5 = 1^2+2^2

79 = +1^2+2^2+3^2-4^2-5^2+6^2-7^2 + 8^2 - 9^2+10^2 - 11^2 +12^2 +13^2 + 14^2 - 15^2-16^2+17^2-18^2-19^2-20^2+21^2+22^2

90 = -(-(-(-(-(-(-(-(-(+1^2+2^2)+3^2)+4^2)+5^2+6^2+7^2)+8^2)+9^2+10^2)+11^2+12^2)+13^2+14^2)+15^2)

In this mode n can be entered as input and the app will give the required expression for n.

App will take input between 1 to 100.

Play with this app to have ideas about some of the peculiar properties of numbers.

This app is ABSOLUTELY FREE, contains NO-ADS or IN-APP PURCHASES.

In case of any bug please email me.