)Father and his two sons
-
Phlembac Adib Hasan
- Posts:1016
- Joined:Tue Nov 22, 2011 7:49 pm
- Location:127.0.0.1
- Contact:
One man has two sons.His age is less than $131$.At present he and his sons' ages are powers of a same prime.One year ago all of their ages were primes.Now find all possible ages of the sons.(Don't forget to check the cases )
)Welcome to BdMO Online Forum. Check out Forum Guides & Rules
-
sakibtanvir
- Posts:188
- Joined:Mon Jan 09, 2012 6:52 pm
- Location:24.4333°N 90.7833°E
Re: Father and his two sons
Just find all Mersenne Primes.... 
An amount of certain opposition is a great help to a man.Kites rise against,not with,the wind.
-
nafistiham
- Posts:829
- Joined:Mon Oct 17, 2011 3:56 pm
- Location:24.758613,90.400161
- Contact:
Re: Father and his two sons
yap.the ages are $4,8,32$
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
-
Phlembac Adib Hasan
- Posts:1016
- Joined:Tue Nov 22, 2011 7:49 pm
- Location:127.0.0.1
- Contact:
Re: Father and his two sons
Give them pairwisely. 
Welcome to BdMO Online Forum. Check out Forum Guides & Rules
-
nafistiham
- Posts:829
- Joined:Mon Oct 17, 2011 3:56 pm
- Location:24.758613,90.400161
- Contact:
Re: Father and his two sons
father's age is $32$Phlembac Adib Hasan wrote:Give them pairwisely.
the sons' ages are $8,4$
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
-
Phlembac Adib Hasan
- Posts:1016
- Joined:Tue Nov 22, 2011 7:49 pm
- Location:127.0.0.1
- Contact:
Re: Father and his two sons
That's why I told to check the cases.The sons can be twin or not.So you must write all possible ages separately.
Welcome to BdMO Online Forum. Check out Forum Guides & Rules
Re: Father and his two sons
অন্য প্রাইমগুলো কেন হবে না, সেটা এম্নিতেই বোঝা যায়, কারন বিজোড় সংখ্যার পাওয়াড় যেকোনো কিছু(০র বড়) বিজোড় সংখ্যা। আর বিজোড় সংখ্যা থেকে ১ বিয়োগ করলে সেটা জোড় সংখ্যা হবে। অর্থাৎ প্রাইম একটাই...২
Last edited by Eesha on Thu Feb 09, 2012 6:13 pm, edited 1 time in total.
গণিত অলেম্পিয়াডে প্রাইজ পাওয়াটাই আসল না। প্রাইজ সবসময় পায়না এমন অনেকেও অনেক ভাল।
পরিচিতি
পরিচিতি
-
sakibtanvir
- Posts:188
- Joined:Mon Jan 09, 2012 6:52 pm
- Location:24.4333°N 90.7833°E
Re: Father and his two sons
I am giving a case....It is 127,3,3 . 
An amount of certain opposition is a great help to a man.Kites rise against,not with,the wind.
-
Tahmid Hasan
- Posts:665
- Joined:Thu Dec 09, 2010 5:34 pm
- Location:Khulna,Bangladesh.
Re: Father and his two sons
$127-1=126$,not a primesakibtanvir wrote:I am giving a case....It is 127,3,3 .
বড় ভালবাসি তোমায়,মা
-
nafistiham
- Posts:829
- Joined:Mon Oct 17, 2011 3:56 pm
- Location:24.758613,90.400161
- Contact:
Re: Father and his two sons
kind'a tricky.(আমি এইগুলাতে সবসময়ই মাইর খাইPhlembac Adib Hasan wrote:That's why I told to check the cases.The sons can be twin or not.So you must write all possible ages separately.
) \[(32,8,8)(32,4,4)(32,8,4)\]
missed this one.sakibtanvir wrote:ohoho sorry i gave the ex- age,present one would be,$127+1,3+1,3+1=128,4,4$...Now i can smile
Last edited by nafistiham on Wed Feb 08, 2012 10:45 pm, edited 2 times in total.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.