Post mathematic related questions here

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mastercool8695

Cyborg Agent
Re: mathematic related questions

Vignesh B said:
Ok, my bad.
Care to explain the answer in brief? :p

One from my side too -
How many pairs of integers are there such that a^2 + 6b^2 and b^2+6a^2 are perfect squares?
Source : I found it in one of my books.
Click to expand...

here you go..

*www.quora.com/Mathematics/How-many-pairs-of-integers-are-there-such-a-2-+-6b-2-and-b-2+6a-2-are-perfect-squares-from-Brilliant-org

this one :
July 3, 1977 is a sunday, then July 3,1970 was ??

A) wednesday
B) friday
C) sunday
D) tuesday

anyways, found this..
*www-history.mcs.st-and.ac.uk/HistTopics/Pell.html
 
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M

mastercool8695

Cyborg Agent
Re: mathematic related questions

no..
if i write the answer so early, i cant have an explaination..
still its not sunday.
so its just three choices now..
i really dont know what theory will strike the question directly, but some surely, will :wink:
 
OP
rst

rst

Youngling
Re: mathematic related questions

mastercool8695 said:
this one :
July 3, 1997 is a sunday, then July 3,1970 was ??

A) wednesday
B) friday
C) sunday
D) tuesday
Click to expand...

It should be Monday But there is no such option
------------------------------------------------------------
There are 27 years from July 3,1997 to July 3, 1970
out of them 7 are leap years
So 20 normal years and 7 leap years

In above question we are going bacward
In normal year ,we go 1 day backward
In leap year we go 2 days backward

total =(20 x 1) + (7 x 2)
=34

34 gives remainder 6 when divided by 7
So we go 6 days backward (or 1 day forward)

So answer is MONDAY
 
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M

mastercool8695

Cyborg Agent
Re: mathematic related questions

^^ sorry, posted 1977 as 1997
sorry..

post edited now..

anyways, your explaination was great.. thanks..
:clap2:
 
OP
rst

rst

Youngling
Re: mathematic related questions

mastercool8695 said:
this one :
July 3, 1977 is a sunday, then July 3,1970 was ??

A) wednesday
B) friday
C) sunday
D) tuesday
Click to expand...

Then ans is Friday

explanation is same as above
----------------------------------------
There are 7 years from July 3,1977 to July 3, 1970
out of them 2 are leap years
So 5 normal years and 2 leap years

In above question we are going bacward
In normal year ,we go 1 day backward
In leap year we go 2 days backward

total =(5 x 1) + (2 x 2)
=9

9 gives remainder 2 when divided by 7
So we go 2 days backward

So answer is FRIDAY
 
M

mastercool8695

Cyborg Agent
Re: mathematic related questions

yup..
thanks.
check this and post your contribution..
*www.thinkdigit.com/forum/education/173487-informative-mathematical-theories.html
 
M

mastercool8695

Cyborg Agent
Re: mathematic related questions

yup..
i know..
the questions from the starting of that book are quite easy,
but i couldn't fit the correct method..
thats why..
 
OP
rst

rst

Youngling
Re: mathematic related questions

----------------------------------------------------------------------------------------------------------------------
NEW OBJECTIVE QUESTION

*img836.imageshack.us/img836/1482/nextno.png

Plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
----------------------------------------------------------------------------------------------------------------------
 
OP
rst

rst

Youngling
Re: mathematic related questions

mastercool8695 said:
*i.imgur.com/FMKAwY1.png
Click to expand...

Ans is B
----------------------------------------------------------------------------------------

A) It is not true
Counter example :-
Let a=2 ,b=3 and n=4
aⁿ +bⁿ =97 ( prime)
 
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darkv0id

darkv0id

Journeyman
Re: mathematic related questions

^ I don't think you understood the question; it's not asking whether a^n+b^n will be prime when one the 4 four choices is true, but rather which of the choices will be true if we already know that a^n+b^n is prime.
 
Niilesh

Niilesh

Padawan
Re: mathematic related questions

rst said:
Ans is (D)
----------------------------------------------------------------------------------------

A) It is not true
Counter example :-
Let a=3 ,b=5 and n=2
aⁿ +bⁿ =34 (not prime)

B) It is not true
Counter example :-
Let a=2 ,b=4 and n=8(power of 2)
aⁿ +bⁿ =even number(not prime)

C)It is not true
Counter example :-
Let a=2 ,b=4 and n=6(even number)
aⁿ +bⁿ =even number(not prime)
Click to expand...
The answer did not say that it will be true for all values of a,b if the conditions on 'n' are satisfied. So you need to give am example in which the condition for n is not satisfied and it is a prime number to prove that the option is wrong :)
 
OP
rst

rst

Youngling
Re: mathematic related questions

darkv0id said:
^ I don't think you understood the question; it's not asking whether a^n+b^n will be prime when one the 4 four choices is true, but rather which of the choices will be true if we already know that a^n+b^n is prime.
Click to expand...

Yeah
you are right

I have edited my previous answer
 
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OP
rst

rst

Youngling
Re: mathematic related questions

Other method
------------------------------------------------------------------
aⁿ+bⁿ is prime number
where n is positive integer other than 1
here n can be even or odd

case 1:- If n is odd
aⁿ+bⁿ =prime number
(a+b) (aⁿ⁻¹ - aⁿ⁻² b +................+(-1)ⁿ⁻¹ bⁿ⁻¹ ) =prime number
Not possible as here prime number is product of two numbers

case 2:- If n is even

I)Let n =2m where m=odd
aⁿ+bⁿ = prime number
a^2m+ b^2m = prime number
(a² )^m+(b² )^m = prime number
so aⁿ+bⁿ can't be prime number (by case 1)

Hence aⁿ+bⁿ = prime number is only possible if n=2m where m is even
i.e n= 4,8,12,16,20,24,………………………………

C) possible n=12,20,24,.......................
They can be expressed as
12=3 x 8
20= 5x 4
24=3 x 8
.
.
similar to case 2(I) not prime number

B)here possible values of n =4,8,16,...................
if aⁿ+bⁿ = prime number
then it will definitely be prime number for these values of n
 
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OP
rst

rst

Youngling
Re: mathematic related questions

if aⁿ+bⁿ = prime number
then n will power of 2

don't do it reverse manner
 
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