Question Number 104497 by PengagumRahasiamu last updated on 21/Jul/20

Commented bymr W last updated on 22/Jul/20

Q2:  a≤2  ?

Commented byPengagumRahasiamu last updated on 22/Jul/20

Non-negative integer Sir

Answered by mr W last updated on 22/Jul/20

suppose a,b,...∈N  Q1:  (x+x^2 +x^3 +x^4 +x^5 +x^6 )^4   =x^4 (1+x+x^2 +x^3 +x^4 +x^5 )^4   =((x^4 (1−x^6 )^4 )/((1−x)^4 ))  =x^4 (1−4x^6 +6x^(12) −4x^(18) +x^(24) )Σ_(k=0) ^∞ C_3 ^(k+3) x^k   coefficient of x^(20)  term:  C_3 ^(19) −4×C_3 ^(13) +6×C_3 ^7 =35  ⇒35 tuples    Q2:  0 tuples if a≤2  since 2+3+4+5+6+7=27<30  2520 tuples if a≥1