A New Family of Filtration S+5 in The Stable Homotopy Groups of Spheres

In this article, by the algebraic method, the author proves the existence of a new nontrivial family of filtration s+5 in the stable homotopy groups of spheres πrS, which is represented by in the Adams spectral sequence, where r=q(pm+pn+(s+3)p2+(s+2)p+(s+1))-5,  t=pmq+pnq+(s+3)p2q+(s+2)pq+(s+1)q+s,p≥n+2>5,0≤s<p-3,q=2(p-1).