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ATTENTION !  May be best viewed by INTERNET EXPLORER 5.0 or HIGHER
THEOREM OF EL'HAYY2  STATES THAT ;

Ratio  Hayy2(n) -->1  ,   as n-->Infinity  ,  where  Hayy2(n) is  defined  as below .
(SUM OF THE POWERS , EQUAL  TO  A  POWER  AT INFINITY)   theorem  is  analysed  in following .

Let   (d , m1 , m2  , t)   are  any  finite integers  , then the functions  a1(n) , a2(n) , b(n)
are defined as  follows where    n    is  another integer  going  to  infinity.
and         

 Binomial coefficient  C(x,y)  is given by --->    

In  fact  theorem  of  El'Hayy2  may  be  obtained from  El'KAyyum


It is obvious that anybody may play with the summation limits , since it doesn't make any difference as one of the variables
in the summation limits goes to infinity. But before doing this we strongly advice to think carefully. Because  there is a
reason for these strange limits; as you approximate one or two of the variables to one or  zero , you may lose some of the
correct answers on  singular  points ;  Such as  (d=1 , t=1 , n=1 ) . You will discover some additional singular points as
you exprience  more ond more on these functions. After all , the success of a theorem or a formula depends on the output
that it produces on any odd or singular input that is given to it.
 
t > d   for converging
For  finite  values  of   n ,  Hayy2(n)   is  an  almost  ONE  .  At   n = Infinity ,  Hayy2(n)   is  exactly   ONE.

For d=1 , we have the condition of  (FLT) type equations . So , for some values of  the integers  a1(n) , a2(n)  , b(n)   at   infinity , we  indeed have a solution for  (FLT).  ; 
If    d=1    then  ;    a1(n)t + a2(n) t  = b(n) t    ,      at    n = Infinity
 
For finite values of  n ;  the integers   a1(n)  , a2(n)  , b(n)  --  almost satisfy the  FLT , for  the  powers of  t .  Therefore  a1(n)  ,  a2(n)  ,  b(n)    will  be  called ,  a set of 
almost  FLT  integers   of   the   order   t  .  As  n => Infinity,   almost   FLT    integers   of   order    t  , 
will  turn out to be exact  FLT  integers  of   the  order  t .   
Please click here to see a typical set of almost  FLT  integers of order 5
Please click here  to see that    for the above set.

ALMOST is a concept in mathematics
for more information on this concept please refer to the following  links;
ALMOST integer
ALMOST prime
ALMOST alternating link
ALMOST alternating knot
ALMOST everywhere
ALMOST perfect number
Of course there is  no  almost  FLT  integers  in  these  links, since this
ALMOST  concept  is  a  new  one.
We should present our gratitudes to Professor Eric W. Weisstein for his immense work in math and science to prepare these links

          We  should  also  give  our  thanks to  Professor  Andrew  Wiles ,  since  for
finite integers of , [a1(n) , a2(n)  , b(n)]  and  t  ; he proved that there  is  no  exact
solution  for the system.
          But for integers  of  [a1(n) , a2(n)  , b(n)]  going  to  infinity according  to  a
certain rule  and  with  finite value of  t=2,3,4......] , it  is seen here that , there  is
an  approached  solution . We  think  that  this fact  deserves  an  attention  from mathematical  community.

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